electro-magnetismo y mecánica-en-ingeniería y ecuaciones-en-derivadas-parciales y mecánica-en-física y mecánica-de-fluidos

Examen de electro-magnetismo:

Principio:

E(x,y,z) = qk·(1/r)^{3}·a·< x^{2},y^{2},z^{2} >

E(yz,zx,xy) = qk·(1/r)^{4}·a^{2}·< (yz)^{2},(zx)^{2},(xy)^{2} >

Ley:

div[ E(x,y,z) ] = ?

Anti-div[ E(yz,zx,xy) ] = ?

Ley:

Anti-Potencial[ E(x,y,z) ] = ?

Potencial[ E(yz,zx,xy) ] = ?

Ley: [ de corrección del examen ]

div[ E(x,y,z) ] = d_{x(yz)}^{2}[ Anti-Potencial[ E(x,y,z) ] ]

Anti-div[ E(yz,zx,xy) ] = d_{x(yz)}^{2}[ Potencial[ E(yz,zx,xy) ] ]

Ley:

R·d_{t}[q(t)]+(-C)·p(t) = W·f(ut)·e^{ut}

p(t) = W·( 1/(uR·d_{ut}[f(ut)]+(-C)·f(ut)) )·f(ut)·e^{ut}

q(t) = W·( ut /o(ut)o/ (uR·f(ut)+(-C)·int[ f(ut) ]d[ut]) ) [o(ut)o] f(ut) [o(ut)o] e^{ut}

Ley:

R·d_{t}[q(t)]+C·p(t) = W·f(ut)·e^{(-1)·ut}

p(t) = W·( 1/((-u)·R·d_{ut}[f(ut)]+C·f(ut)) )·f(ut)·e^{(-1)·ut}

q(t) = W·( ut /o(ut)o/ ((-u)·R·f(ut)+C·int[ f(ut) ]d[ut]) ) [o(ut)o] f(ut) [o(ut)o] e^{(-1)·ut}

Ley:

Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>

Si d[M_{1}(t)] = (1/2)·mgx·(1/s)^{2}·cos(nw)·d[w] ==>

M_{1}(t) = (1/2)·mg·(x/n)·(1/s)^{2}·sin(nw)

Si d[ d[M_{2}(t)] ] = mg·(1/s)^{2}·sin(nw)·cos(nw)·d[y]d[w] ==>

M_{2}(t) = mg·(y/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}

M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( I_{cx}/I_{cy} ) & I_{cx} [< I_{cy} )

Ley:

Sea d_{t}[ I_{c} ] = 0 ==>

Si d[M_{1}(t)] = (1/2)·I_{c}·u^{2}·cos(nw)·d[w] ==>

M_{1}(t) = (1/2)·I_{c}·u^{2}·(1/n)·sin(nw)

Si d[ d[M_{2}(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>

M_{2}(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}

M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( ( 1/ln( aI_{c}·(1/(md)) ) ) ) & aI_{c} >] md·e )

Ley: [ del calor electro-magnético ]

div[ E_{e}(x,y,t) ] = (-2)·(1/c)·B_{e}(x,y,t)

Deducción:

E_{e}(x,y,t)+int[ B_{e}(x,y,t) ]d[t] = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·( cos(w) )^{2}

y(t) = ct·( sin(w) )^{2}

div[ E_{e}(x,y,t) ]+div[ inr[ B_{e}(x,y,t) ]d[t] ] = 0^{2}

div[ int[ B_{e}(x,y,t) ]d[t] ] = ( 1/(d[x]+d[y]) )·(d[x]+d[y]) [o] div[ int[ B_{e}(x,y,t) ]d[t] ]

div[ E_{e}(x,y,t) ]+2·(1/c)·B_{e}(x,y,t) = 0^{2}

div[ E_{e}(x,y,t) ] = (-2)·(1/c)·B_{e}(x,y,t)

Ley: [ del calor gravito-magnético ]

div[ E_{g}(x,y,t) ] = (-2)·(1/c)·B_{g}(x,y,t)

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

u(x,y,(1/u)) = K(ax,ay)

u(x,y,t) = ( (1+(-1)·ut)·H(ax,ay)+ut·K(ax,ay) || 1 )·e^{ax+ay+(-1)·act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

u(x,y,(1/u)) = K(ax,ay)

u(x,y,t) = ( (1+(-1)·ut)·H(ax,ay)+ut·K(ax,ay) || 1 )·e^{ax+ay+act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(0,0,t) = f(ut)

u(p,q,t) = g(ut)

u(x,y,t) = ...

... ( (1/2)·( (1+(-1)·(x/p))·f(ut)+(1+(-1)·(y/q))·f(ut) )+(1/2)·( (x/p)·g(ut)+(y/q)·g(ut) ) || 1 )·...

... e^{ax+ay+(-1)·act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(0,0,t) = f(ut)

u(p,q,t) = g(ut)

u(x,y,t) = ...

... ( (1/2)·( (1+(-1)·(x/p))·f(ut)+(1+(-1)·(y/q))·f(ut) )+(1/2)·( (x/p)·g(ut)+(y/q)·g(ut) ) || 1 )·...

... e^{ax+ay+act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(0,q,t) = f(ut)

u(p,0,t) = g(ut)

u(x,y,t) = ?

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(0,q,t) = f(ut)

u(p,0,t) = g(ut)

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ...

... (1/2)·( e^{ax+ay+ac·it || ln( H(ax,ay) )+act}+e^{ax+ay+ac·it || ln( H(ax,ay) )+(-1)·act} )

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ...

... (1/2)·( e^{ax+ay+act || ln( H(ax,ay) )+act}+e^{ax+ay+act || ln( H(ax,ay) )+(-1)·act} )

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(0,y,0) = F(ay)

u(r,y,0) = G(ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(0,y,0) = F(ay)

u(r,y,0) = G(ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(x,y,0)] = h(ax,ay)

u(x,y,t) = (1/2)·sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·act·0 || (4t)^{(1/2)}]-[h(ax,ay)+act·0 || (4t)^{(1/2)}][ w ]d[w] ]·e^{ax+ay+ac·it || 0}

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(x,y,0)] = h(ax,ay)

u(x,y,t) = (1/2)·sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·act·0 || (4t)^{(1/2)}]-[h(ax,ay)+act·0 || (4t)^{(1/2)}][ w ]d[w] ]·e^{ax+ay+act || 0}

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(0,y,0)] = ac·f(ay)

d_{t}[u(r,y,0)] = ac·g(ay)

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(0,y,0)] = ac·f(ay)

d_{t}[u(r,y,0)] = ac·g(ay)

u(x,y,t) = ?

Motores a combustión de explosión acotada:

Ley:

Sea d[I_{c}] = (1/s)^{2}·Mrv·d[t] ==>

Si (I_{c}/2)·d_{t}[w]^{2} = qgh·cos(ut) ==>

x(t) = (M/(md))·(1/s)^{2}·rvt

w(t) = (1/u)·( 2qgh·(1/(Mrv))·us^{2}·( ln(ut) [o(ut)o] sin(ut) ) )^{[o(ut)o] (1/2)}

(1/u) [< t [< (pi/u)

Ley:

Sea d[I_{c}] = (1/s)^{2}·Mrgt·d[t] ==>

Si (I_{c}/2)·d_{t}[w]^{2} = qgh·sin(ut) ==>

x(t) = (M/(md))·(1/s)^{2}·rg·(1/2)·t^{2}

w(t) = (1/u)·( 4qgh·(1/(Mrg))·(us)^{2}·( (1/(ut)) [o(ut)o] cos(ut) ) )^{[o(ut)o] (1/2)}

(1/u) [< t [< (pi/(2u))

Los rusos tienen misiles de fusión nuclear,

en toroide de cuerda,

y polígono de propulsión y de ocultación al radar.

Pero se puede detectar con un radar poligonal.

Teorema:

( cos(w) )^{4}+(-1)·( sin(w) )^{4}+i·sin(2w) = e^{2iw}

Teorema:

( cos(w) )^{4}+( sin(w) )^{4}+(1/2)·( sin(2w) )^{2} = 1

Ley:

Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>

Si d[ d[M(t)] ] = qg·(1/s)^{2}·sin(nw)·cos(nw)·d[x]d[w] ==>

M(t) = qg·(x/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}

(I_{c}/2)·d_{t}[w]^{2} = qgx·(1/(ns))^{2}·(1/4)·( nw+(-1)·(1/2)·sin(2nw) )

x(t) = I_{c}·(1/(md))

w(t) = (1/n)·Anti-[ ( s /o(s)o/ ( (1/4)·s^{2}+(1/8)·cos(2s) ) )^{[o(s)o](1/2)}]-( ...

... ( (1/(md))·qg )^{(1/2)}·(1/s)·t )

Ley:

Sea d_{t}[ I_{c} ] = 0 ==>

Si d[ d[M(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>

M(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}

(I_{c}/2)·d_{t}[w]^{2} = I_{c}·u^{2}·ln(ax)·(1/n)^{2}·(1/4)·( nw+(-1)·(1/2)·sin(2nw) )

x(t) = I_{c}·(1/(md))

w(t) = (1/n)·Anti-[ ( s /o(s)o/ ( (1/4)·s^{2}+(1/8)·cos(2s) ) )^{[o(s)o](1/2)}]-( ...

... ( ln( aI_{c}·(1/md) ) )^{(1/2)}·ut )

Ecuaciones de densidades:

Leyes de agua y aceite:

Ley: 

d_{x}[u(x,y)]+d_{y}[u(x,y)] = (m/V)·xy

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·( (m/(4V))·yx^{2} || (m/(4V))·xy^{2} || m )

Ley:

d_{x}[u(x,y)]+d_{y}[u(x,y)] = (-V)·m·( 1/(xy) )^{2}

u(x,0) = m·F(ax)

u(x,r) = m·G(ax)

u(x,y) = ( (1+(-1)·(y/r))·F(ax)+(y/r)·G(ax) || 1 )·( (V/2)·( m/(xy^{2}) ) || (V/2)·( m/(yx^{2}) ) || m )

Ley: [ de ola de mar ]

d_{x}[u(x,y)]+d_{y}[u(x,y)] = m·(1/a)·(1/(xy))

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·( (1/2)·(m/(ay))·ln(ax) || (1/2)·(m/(ax))·ln(ay) || m )

Ley: 

d_{x}[u(x,y)]+d_{y}[u(x,y)]+a·u(x,y) = (m/V)·xy

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·....

... ( (m/(6V))·yx^{2} || (m/(6V))·xy^{2} || (1/(3V))·(m/a)·xy || m )

Ley:

d_{x}[u(x,y)]+d_{y}[u(x,y)]+a·u(x,y) = (-V)·m·( 1/(xy) )^{2}

u(x,0) = m·F(ax)

u(x,r) = m·G(ax)

u(x,y) = ( (1+(-1)·(y/r))·F(ax)+(y/r)·G(ax) || 1 )·...

... ( (V/3)·( m/(xy^{2}) ) || (V/3)·( m/(yx^{2}) ) || (-1)·(V/3)·(m/a)·( 1/(xy) )^{2} || m )

Teorema:

f(a) = f(a)·(1/z)^{0}

(1/0!)·d_{a}[f(a)] = (-1)·d_{a}[f(a)]·(1/z)

(1/1!)·d_{aa}^{2}[f(a)] = d_{aa}^{2}[f(a)]·(1/z)^{2}

(1/2!)·d_{aaa}^{3}[f(a)] = (-1)·d_{aaa}^{3}[f(a)]·(1/z)^{3}

Demostración:

Sea z(t) = e^{(-t)}+a ==>

Se deriva y se integra quedando-se igual:

int[t = 0]-[1][ f(a)/(a+(-z)) ]d[z] = int-int[ (-1)·d_{a}[f(a)]·(1/z) ]d[z]d[a] = f(a)

int[ (-1)·d_{a}[f(a)]·(1/z) ]d[z] = d_{a}[f(a)]

int-int[t = 0]-[1][ f(a)/(a+(-z))^{2} ]d[z]d[z] = ...

... int-int-int-int[ d_{aa}^{2}[f(a)]·(1/z)^{2} ]d[z]d[z]d[a]d[a] = f(a)

int-int[ d_{aa}^{2}[f(a)]·(1/z)^{2} ]d[z]d[z] = d_{aa}^{2}[f(a)]

int-int-int[t = 0]-[1][ 2·f(a)/(a+(-z))^{3} ]d[z]d[z]d[z] = ...

... int-int-int-int-int-int[ (-1)·2·d_{aaa}^{2}[f(a)]·(1/z)^{3} ]d[z]d[z]d[z]d[a]d[a]d[a] = f(a)

int-int-int[ (-1)·2·d_{aaa}^{3}[f(a)]·(1/z)^{3} ]d[z]d[z]d[z] = d_{aaa}^{3}[f(a)]

Series de Laurent:

Sea z(x) = e^{x} ==>

e^{z} = 1+sum[k = 1]-[oo][ (1/k)·(x/z)^{k} ]

( 1/(1+(-z)) ) = 1+sum[k = 1]-[oo][ (k+(-1))!·(x/z)^{k} ]

z·( 1/(1+(-z))^{2} ) = 1+sum[k = 1]-[oo][ k!·(x/z)^{k} ]

e-pos[m](z) = m+sum[k = 1]-[oo][ ( 1+m·(1/k) )·(x/z)^{k} ]

e-neg[m](z) = (-m)+sum[k = 1]-[oo][ ( 1+(-m)·(1/k) )·(x/z)^{k} ]

octopus(z) = 1+sum[k = 1]-[oo][ (k+1)!·(1/k)·(x/z)^{k} ]

d_{x}[ octopus(z) ] = sum[k = 1]-[oo][ (k+2)!·(1/k)·(x/z)^{k} ]

física-en-ingeniería y mecánica-de-fluidos y cálculo-integral-geometría y mecánica-en-física

Preliminares:

Principio:

[Ev][ d_{t}[x] = v ]

Ley:

x(t) = vt+h

Deducción:

x(t) = int[ d_{t}[x] ]d[t] = int[ v ]d[t] = v·int[ d[t] ] = vt+h

Principio:

[Eg][ d_{tt}^{2}[x] = g ]

Ley:

Si g = 0 ==> [Ev][ d_{t}[x] = v ]

Ley:

d_{t}[x] = gt+v

x(t) = g·(1/2)·t^{2}+vt+h

Deducción:

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ g ]d[t] = g·int[ d[t] ] = gt+v

x(t) = int[ d_{t}[x] ]d[t] = int[ gt+v ]d[t]  = int[ gt ]d[t]+int[ v ]d[t] = g·int[ t ]d[t]+v·int[ d[t] ] = ...

... g·(1/2)·t^{2}+vt+h

Ley:

Sea x(t) = ( r^{n}+(vt)^{n} )^{(1/n)} ==>

d_{t}[x] = ( r^{n}+(vt)^{n} )^{(1/n)+(-1)}·(vt)^{n+(-1)}·v

Deducción:

d_{t}[ ( r^{n}+(vt)^{n} )^{(1/n)} ] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·...

... d_{vt}[ r^{n}+(vt)^{n} ]·d_{t}[vt] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·...

... ( d_{vt}[ r^{n} ]+d_{vt}[ (vt)^{n} ] )·d_{t}[vt] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·...

... ( 0+d_{vt}[ (vt)^{n} ] )·d_{t}[vt] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·d_{vt}[ (vt)^{n} ]·d_{t}[vt]

Ley:

Sea d_{t}[x] = ( c^{(1/n)}+(gt)^{(1/n)} )^{n} ==>

x(t) = ( n/(n+1) )·( c^{(1/n)}+(gt)^{(1/n)} )^{n+1} [o(gt)o] ...

... ( 1/(2+(-1)·(1/n)) )·(gt)^{2+(-1)·(1/n)} [o(gt)o] t

Deducción:

g·d_{gt}[ ( ( n/(n+1) )·( c^{(1/n)}+(gt)^{(1/n)} )^{n+1} [o(gt)o] ...

... ( 1/(2+(-1)·(1/n)) )·(gt)^{2+(-1)·(1/n)} ) [o(gt)o] t ] = ...

g·d_{gt}[ ( ( n/(n+1) )·( c^{(1/n)}+(gt)^{(1/n)} )^{n+1} ]·...

... d_{gt}[ ( 1/(2+(-1)·(1/n)) )·(gt)^{2+(-1)·(1/n)} ]·d_{gt}[t] ] = ...

... g·( c^{(1/n)}+(gt)^{(1/n)} )^{n}·d_{gt}[t] = ( c^{(1/n)}+(gt)^{(1/n)} )^{n}

Ley:

Sea y(t,x) = ax^{2} ==>

Si d_{t}[x] = v ==>

d_{tt}^{2}[y(t,x)] = 2av^{2}

d_{t}[y(t,x)] = 2av^{2}·t

y(t,x) = a·(vt)^{2}

Deducción:

d[y(t,x)] = 2ax·d[x]

d_{t}[y(t,x)] = 2ax·d_{t}[x]

d_{tt}^{2}[y(t,x)] = 2a·( d_{t}[x]^{2}+x·d_{tt}^{2}[x] )

x(t) = int[ d_{t}[x] ]d[t] = int[ v ]d[t] = v·int[ d[t] ] = vt 

Ley:

Sea y(t,x) = ax^{2} ==>

Si d_{tt}^{2}[x] = g ==>

d_{tt}^{2}[y(t,x)] = 6ag^{2}·(1/2)·t^{2}

d_{t}[y(t,x)] = 2ag·(1/2)·t^{2}·gt

y(t,x) = a·( g^{2}·(1/4)·t^{4} )

Deducción:

d[y(t,x)] = 2ax·d[x]

d_{t}[y(t,x)] = 2ax·d_{t}[x]

d_{tt}^{2}[y(t,x)] = 2a·( d_{t}[x]^{2}+x·d_{tt}^{2}[x] )

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ g ]d[t] = g·int[ d[t] ] = gt

x(t) = int[ d_{t}[x] ]d[t] = int[ gt ]d[t] = g·int[ t ]d[t] = g·(1/2)·t^{2}

t = (2x/g)^{(1/2)}

Ley:

Sea 2·( sin(w) )^{2} = ( 1+(-1)·cos(2w) ) ==>

Sea ( d_{t}[x] = v·sin(ut) & d_{t}[y] = v·( 1+(-1)·cos(ut) ) ==>

d_{t}[r] = 2v·sin((ut)/2)

r(0,2pi) = 8v·(1/u)

Ley:

Sea 2·( cos(w) )^{2} = ( 1+cos(2w) ) ==>

Sea ( d_{t}[x] = v·sin(ut) & d_{t}[y] = v·( 1+cos(ut) ) ==>

d_{t}[r] = 2v·cos((ut)/2)

r((-pi),pi) = 8v·(1/u)

Globos y Drones:

Ley:

Sea d_{t}[x] = uy ==>

Si d_{t}[y] = v ==>

x(y) = u·(1/v)·(1/2)·y^{2}

d_{tt}^{2}[x] = uv

Ley:

Sea d_{t}[x] = uy ==>

Si d_{t}[y] = gt ==>

x(y) = ug·(1/6)·( (2/g)·y )^{(3/2)}

d_{tt}^{2}[x] = ugt

---------------------------------------------------

Procedimiento en coordenadas cartesianas:

---------------------------------------------------

Principio: [ de Fuerza ]

[EF_{k}][ m·d_{tt}^{2}[x] = sum[k = 1]-[n][ F_{k} ] ]

Ley: [ de Impulsión ]

[Ep_{k}][ m·d_{t}[x] = sum[k = 1]-[n][ p_{k} ] ]

Deducción:

int[ m·d_{tt}^{2}[x] ]d[t] = m·int[ d_{tt}^{2}[x] ]d[t] = m·d_{t}[x]

int[ sum[k = 1]-[n][ F_{k} ] ]d[t] = sum[k = 1]-[n][ int[ F_{k} ]d[t] ] = sum[k = 1]-[n][ p_{k} ]

Ley: [ de Energía ]

[EU_{k}][ (m/2)·d_{t}[x]^{2} = sum[k = 1]-[n][ U_{k} ] ]

Deducción:

int[ m·d_{tt}^{2}[x] ]d[x] = int[ m·d_{tt}^{2}[x]·d_{t}[x] ]d[t] = (m/2)·d_{t}[x]^{2}

int[ sum[k = 1]-[n][ F_{k} ] ]d[x] = sum[k = 1]-[n][ int[ F_{k} ]d[x] ] = sum[k = 1]-[n][ U_{k} ]

Ley: [ de Potencia ]

[EN_{k}][ (m/u)·d_{t}[x]^{[o(ut)o] 2} = sum[k = 1]-[n][ N_{k} ] ]

Deducción:

int[ m·d_{tt}^{2}[x] ]d[ d_{t}[x] ] = int[ (m/u)·d_{tt}^{2}[x]^{2} ]d[ut] = (m/u)·d_{t}[x]^{[o(ut)o] 2}

int[ sum[k = 1]-[n][ F_{k} ] ]d[ d_{t}[x] ] = sum[k = 1]-[n][ int[ F_{k} ]d[ d_{t}[x] ] ] = ...

... sum[k = 1]-[n][ N_{k} ]

Fuerza constante:

Ley:

Sea F(t) = F ==>

d_{t}[x] = (F/m)·t

x(t) = (F/m)·(1/2)·t^{2}

Deducción:

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ (F/m) ]d[t] = (F/m)·int[ d[t] ] = (F/m)·t

x(t) = int[ d_{t}[x] ]d[t] = int[ (F/m)·t ]d[t] = (F/m)·int[ t ]d[t] = (F/m)·(1/2)·t^{2}

Ley:

Sea F(t) = F ==>

U(x) = Fx

(m/2)·d_{t}[x]^{2} = U(x)

Deducción:

U(x) = int[ F ]d[x] = F·int[ d[x] ] = Fx

(m/2)·d_{t}[x]^{2} = (m/2)·( (F/m)·t )^{2} = F·( (F/m)·(1/2)·t^{2} ) = Fx = U(x)

Ley:

Sea F(t) = F ==>

N(d_{t}[x]) = F·d_{t}[x]

(m/u)·d_{t}[x]^{[o(ut)o] 2} = N(d_{t}[x])

Deducción:

N(d_{t}[x]) = int[ F ]d[ d_{t}[x] ] = F·int[ d[ d_{t}[x] ] ] = F·d_{t}[x]

(m/u)·d_{t}[x]^{[o(ut)o] 2} = (m/u)·( (F/m)·t )^{[o(ut)o] 2} = int[ (m/u)·(F/m)^{2} ]d[ut] = ...

... F·( (F/m)·t ) = F·d_{t}[x] = N(d_{t}[x])

Fuerza lineal de carga variable:

Ley:

Sea F(t) = Itg ==>

d_{t}[y] = (1/m)·Ig·(1/2)·t^{2}

y(t) = (1/m)·Ig·(1/6)·t^{3}

Deducción:

d_{t}[y] = int[ d_{tt}^{2}[y] ]d[t] = int[ (1/m)·Itg ]d[t] = (1/m)·Ig·int[ t ]dt = (1/m)·Ig·(1/2)·t^{2}

y(t) = int[ d_{t}[y] ]d[t] = int[ (1/m)·Ig·(1/2)·t^{2} ]d[t] = (1/m)·Ig·(1/2)·int[ t^{2} ]d[t] = ...

... (1/m)·Ig·(1/6)·t^{3}

Ley:

Sea F(t) = Itg ==>

U(y) = (1/m)·(Ig)^{2}·(1/8)·t^{4}

(m/2)·d_{t}[y]^{2} = U(y)

Deducción:

U(y) = int[ Itg ]d[y] = int[ Itg d_{t}[y] ]d[t] = int[ (1/m)·( Ig )^{2}·(1/2)·t^{3}· ]d[t] = ...

... (1/m)·( Ig )^{2}·(1/8)·t^{4}

(m/2)·d_{t}[y]^{2} = (m/2)·( ( (1/m)·Ig )·(1/2)·t^{2} )^{2} = (1/m)·( Ig )^{2}·(1/8)·t^{4} = U(y)

Ley:

Sea F(t) = Itg ==>

N(d_{t}[y]) = (1/m)·( Ig )^{2}·(1/3)·t^{3}

(m/u)·d_{t}[y]^{[o(ut)o] 2} = N(d_{t}[y])

Deducción:

N(d_{t}[y]) = int[ Itg ]d[ d_{t}[y] ] = int[ (1/m)·Itg d_{tt}^{2}[y] ]d[t] = ...

... int[ (1/m)·( Itg )^{2} ]d[t] = (1/m)·( Ig )^{2}·(1/3)·t^{3}

(m/u)·d_{t}[y]^{[o(ut)o] 2} = (m/u)·( ( (1/m)·Ig )·(1/2)·t^{2} )^{[o(ut)o] 2} = ...

... int[ (1/m)·( Ig )^{2}·t^{2} ]d[t] = (1/m)·( Ig )^{2}·(1/3)·t^{3} = N(d_{t}[y])

Fuerzas de amortiguación y de resistencia de fluido:

Horizontal:

Ley:

m·d_{tt}^{2}[x] = (-k)·x

x(t) = re^{(k/m)^{(1/2)}·it}

Deducción:

m·d_{tt}^{2}[x] = m·d_{t}[ d_{t}[x] ] = m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ] ] = ...

... m·d_{t}[ r·d_{t}[ e^{(k/m)^{(1/2)}·it} ] ] = m·d_{t}[ re^{(k/m)^{(1/2)}·it}·(k/m)^{(1/2)}·i ] = ...

... mr·(k/m)^{(1/2)}·i·d_{t}[ e^{(k/m)^{(1/2)}·it} ] = ...

... mr·( (k/m)^{(1/2)}·i )^{2} e^{(k/m)^{(1/2)}·it} = ...

... (-k)·re^{(k/m)^{(1/2)}·it} = (-k)·x

Ley

m·d_{tt}^{2}[x] = (-b)·d_{t}[x]

d_{t}[x] = ve^{(-1)·(b/m)·t}

Deducción:

m·d_{tt}^{2}[x] = m·d_{t}[ d_{t}[x] ] = m·d_{t}[ ve^{(-1)·(b/m)·t} ] = ...

... mv·d_{t}[ e^{(-1)·(b/m)·t} ] = mv·e^{(-1)·(b/m)·t}·(-1)·(b/m) = ...

... (-b)·ve^{(-1)·(b/m)·t} = (-b)·d_{t}[x]

Ley:

U(x) = (-k)·(1/2)·x^{2}

(m/2)·d_{t}[x]^{2} = U(x)

Deducción:

U(x) = int[ (-k)·x ]d[x] = (-k)·int[ x ]d[x] = (-k)·(1/2)·x^{2}

(m/2)·d_{t}[x]^{2} = (m/2)·( i·(k/m)^{(1/2)}·re^{(k/m)^{(1/2)}·it} )^{2} = ...

... (-k)·(1/2)·( r^{2}·e^{(k/m)^{(1/2)}·2it} ) = (-k)·(1/2)·x^{2} = U(x)

Ley:

N(d_{t}[x]) = (-b)·(1/2)·d_{t}[x]^{2}

(m/u)·d_{t}[x]^{[o(ut)o] 2} = N(d_{t}[x])

Deducción:

N(d_{t}[x]) = int[ (-b)·d_{t}[x] ]d[ d_{t}[x] ] = ...

... (-b)·int[ d_{t}[x] ]d[ d_{t}[x] ] = (-b)·(1/2)·d_{t}[x]^{2}

(m/u)·d_{t}[x]^{[o(ut)o] 2} = (m/u)·( ve^{(-1)·(b/m)·t} )^{[o(ut)o] 2} = ...

... (m/u)·int[ ( (-1)·(b/m)·v )^{2}·e^{(-2)·(b/m)·t} ]d[ut] = ...

... (-b)·(1/2)·( v^{2}·e^{(-2)·(b/m)·t} ) = (-b)·(1/2)·d_{t}[x]^{2} = N(d_{t}[x])

Fuerzas de amortiguación y de resistencia de fluido:

Vertical:

Ley:

m·d_{tt}^{2}[y] = (-k)·y+qg

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·qg

Deducción:

m·d_{tt}^{2}[y] = m·d_{t}[ d_{t}[y] ] = m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it}+(1/k)·qg ] ] = ...

... m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ]+d_{t}[ (1/k)·qg ] ] = ...

... m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ]+0 ] = m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ] = ...

... m·d_{tt}^{2}[ re^{(k/m)^{(1/2)}·it} ] = (-k)·re^{(k/m)^{(1/2)}·it} = ...

... (-k)·re^{(k/m)^{(1/2)}·it}+(-1)·qg+qg = (-k)·( re^{(k/m)^{(1/2)}·it}+(1/k)·qg )+qg = (-k)·y+qg

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+qg

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·qg

Deducción:

m·d_{tt}^{2}[y] = m·d_{t}[ d_{t}[y] ] = m·d_{t}[ ve^{(-1)·(b/m)·t}+(1/b)·qg ] = ...

... m·( d_{t}[ ve^{(-1)·(b/m)·t} ]+d_{t}[ (1/b)·qg ] ) = ...

... m·( d_{t}[ ve^{(-1)·(b/m)·t} ]+0 ) = m·d_{t}[ ve^{(-1)·(b/m)·t} ] = (-b)·ve^{(-1)·(b/m)·t} = ...

... (-b)·ve^{(-1)·(b/m)·t}+(-1)·qg+qg = (-b)·( ve^{(-1)·(b/m)·t}+(1/b)·qg )+qg = (-b)·d_{t}[y]+qg

Obertura de hombros y caderas robótica:

Por amortiguador de retorno con empuje de obertura de fluido.

Ley:

m·d_{tt}^{2}[y] = (-k)·y+( sin(w)·qg+sin(s)·pg )

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·( sin(w)·qg+sin(s)·pg )

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+( sin(w)·qg+sin(s)·pg )

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·( sin(w)·qg+sin(s)·pg )

Estiramiento de rodillas y codos robótica:

Por amortiguador de retorno con empuje de obertura de fluido.

Ley:

m·d_{tt}^{2}[y] = (-k)·y+( F+(-1)·qg )

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·( F+(-1)·qg )

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+( F+(-1)·qg )

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·( F+(-1)·qg )

Motores robóticos que aumentan la fuerza según la carga:

Ley:

m·d_{tt}^{2}[y] = (-k)·y+( Itg+qg )

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·( Itg+qg )

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+( Itg+qg )

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·( Itg+qg )+(-1)·(1/b)^{2}·Ig

----------------------------------------------

Procedimiento en coordenadas polares:

----------------------------------------------

Principio: [ de Inercia angular ]

[EI_{ck}][ mdx = sum[k = 1]-[n][ I_{ck} ] ]

[ d ] = ( metro / ( radian )^{2} )

Ley: [ de Impulsión angular ]

[EL_{k}][ md·d_{t}[x] = sum[k = 1]-[n][ L_{k} ] ]

Deducción:

d_{t}[ mdx ] = md·d_{t}[x] = md·d_{t}[x]

d_{t}[ sum[k = 1]-[n][ I_{ck} ] ] = sum[k = 1]-[n][ d_{t}[ I_{ck} ] ] = ...

... sum[k = 1]-[n][ L_{k} ]

Ley: [ de Fuerza angular ]

[EH_{k}][ md·d_{tt}^{2}[x] = sum[k = 1]-[n][ H_{k} ] ]

Deducción:

d_{t}[ md·d_{t}[x] ] = md·d_{t}[ d_{t}[x] ] = md·d_{tt}^{2}[x]

d_{t}[ sum[k = 1]-[n][ L_{k} ] ] = sum[k = 1]-[n][ d_{t}[ L_{k} ] ] = ...

... sum[k = 1]-[n][ H_{k} ]

Principio: [ de Energía angular ]

[EU_{k}][ I_{c}·(1/2)·d_{t}[w]^{2} = sum[k = 1]-[n][ U_{k} ] ]

Ley:

Sea U(w) = U ==>

Si I_{c} = M·(r/s)^{2} ==> 

x(t) = (M/m)·(1/d)·(r/s)^{2}

w(t) = ( (2/M)·U )^{(1/2)}·(s/r)·t

Deducción:

mdx = M·(r/s)^{2}

I_{c}·(1/2)·d_{t}[w]^{2} = M·(r/s)^{2}·(1/2)·d_{t}[ ( (2/M)·U )^{(1/2)}·(s/r)·t ]^{2} = ...

... M·(r/s)^{2}·(1/2)·( ( (2/M)·U )^{(1/2)}·(s/r)·d_{t}[ t ] )^{2} = ...

... M·(r/s)^{2}·(1/2)·( ( (2/M)·U )^{(1/2)}·(s/r) )^{2} = U

Principio: [ Fundamental de la dinámica angular ]

[EM_{k}][ d_{w}[ U(w) ] = sum[k = 1]-[n][ M_{k} ] ]

[ M_{k} ] = ( Joule / Radian )

Ley:

L(t)·(1/2)·d_{t}[w]+I_{c}·d_{tt}^{2}[w] = sum[k = 1]-[n][ M_{k} ]

Deducción:

d_{w}[ I_{c}·(1/2)·d_{t}[w]^{2} ] = (1/d_{t}[w])·d_{t}[ I_{c}·(1/2)·d_{t}[w]^{2} ] ...

... (1/d_{t}[w])·( d_{t}[ I_{c} ]·(1/2)·d_{t}[w]^{2}+I_{c}·d_{t}[ (1/2)·d_{t}[w]^{2} ] ) = ...

... L(t)·(1/2)·d_{t}[w]+I_{c}·d_{tt}^{2}[w]

Ley: [ de Momento de Fuerza ]

Si d_{t}[ I_{c} ] = 0 ==> 

[EM_{k}][ I_{c}·d_{tt}^{2}[w] = sum[k = 1]-[n][ M_{k} ] ]

Ley: [ de Momento de Impulsión ]

Si d_{t}[ I_{c} ] = 0 ==>

[EK_{k}][ I_{c}·d_{t}[w] = sum[k = 1]-[n][ K_{k} ] ]

Deducción:

int[ I_{c}·d_{tt}^{2}[w] ]d[t] = I_{c}·int[ d_{tt}^{2}[x] ]d[t] = I_{c}·d_{t}[w]

int[ sum[k = 1]-[n][ M_{k} ] ]d[t] = sum[k = 1]-[n][ int[ M_{k} ]d[t] ] = ...

... sum[k = 1]-[n][ K_{k} ]

Ley: [ de Potencia angular ]

Si d_{t}[ I_{c} ] = 0 ==>

[EN_{k}][ (I_{c}/u)·d_{t}[w]^{[o(ut)o] 2} = sum[k = 1]-[n][ N_{k} ] ]

Deducción:

int[ I_{c}·d_{tt}^{2}[w] ]d[ d_{t}[w] ] = int[ (I_{c}/u)·d_{tt}^{2}[w]^{2} ]d[ut] = ...

.. (I_{c}/u)·d_{t}[w]^{[o(ut)o] 2}

int[ sum[k = 1]-[n][ M_{k} ] ]d[ d_{t}[w] ] = sum[k = 1]-[n][ int[ M_{k} ]d[ d_{t}[w] ] ] = ...

... sum[k = 1]-[n][ N_{k} ]

Ley:

Si ( d_{t}[ I_{c} ] = 0 & M(w) = F·(x/s) ) ==> 

d_{t}[w] = (1/I_{c})·F·(x/s)·t

w(t) = (1/I_{c})·F·(x/s)·(1/2)·t^{2}

Deducción:

Problema.

Ley:

Si ( d_{t}[ I_{c} ] = 0 & M(w) = F·(x/s) ) ==> 

U(w) = F·(x/s)·w

I_{c}·d_{t}[w]^{2} = U(w)

Deducción:

U(w) = int[ M(w) ]d[w] = int[ F·(x/s) ]d[w] = F·(x/s)·int[ d[w] ] = F·(x/s)·w

(I_{c}/2)·d_{t}[w]^{2} = (I_{c}/2)·( (1/I_{c})·F·(x/s)·t )^{2} = ...

... F·(x/s)·( (1/I_{c})·F·(x/s)·(1/2)·t^{2} ) = F·(x/s)·w = U(w)

Ley:

Si ( d_{t}[ I_{c} ] = 0 & M(w) = F·(x/s) ) ==> 

N(d_{t}[w]) = F·(x/s)·d_{t}[w]

(I_{c}/u)·d_{t}[w]^{[o(ut)o] 2} = N(d_{t}[w])

Deducción:

N(d_{t}[w]) = int[ M(w) ]d[ d_{t}[w] ] = int[ F·(x/s)·d_{tt}^{2}[w] ]d[t] = ...

... int[ (1/I_{c})·( F·(x/s) )^{2} ]d[t] = (1/I_{c})·( F·(x/s) )^{2}·int[ d[t] ] = ...

... (1/I_{c})·( F·(x/s) )^{2}·t = F·(x/s)·d_{t}[w]

(I_{c}/u)·d_{t}[w]^{[o(u)o] 2} = (I_{c}/u)·( (1/I_{c})·F·(x/s)·t )^{[o(ut)o] 2} = ...

... (I_{c}/u)·int[ ( (1/I_{c})·F·(x/s) )^{2} ]d[ut] = ...

...(1/I_{c})·( F·(x/s) )^{2}·int[ d[t] ] = (1/I_{c})·( F·(x/s) )^{2}·t = ...

... F·(x/s)·d_{t}[w] = N(d_{t}[w])

Inercias angulares constantes:

Principio:

[Ef][ I_{c} = int[ ( (r·f(n))/s )^{2}·d_{n}[m(n)] ]d[n] ]

Ley:

Si f(n) = n^{0} ==> I_{c} = int[ (r/s)^{2}·d_{n}[m(n)] ]d[n]

Si f(n) = (n/r) ==> I_{c} = int[ (n/s)^{2}·d_{n}[m(n)] ]d[n]

Principio:

[Ef][Eg][ I_{c} = int-int[ (1/2)·( ( (r·f(p))/s )^{2}+( (r·g(q))/s )^{2} )·d_{pq}^{2}[m(p,q)] ]d[p]d[q] ]

Ley:

Si ( f(p) = p^{0} & g(q) = q^{0} ) ==> I_{c} = int-int[ (r/s)^{2}·d_{pq}^{2}[m(p,q)] ]d[p]d[q]

Si ( f(p) = (p/r) & g(q) = (q/r) ) ==> ...

... I_{c} = int-int[ (1/2)·( (p/s)^{2}+(q/s)^{2} )·d_{pq}^{2}[m(p,q)] ]d[p]d[q]

Ley:

Sea ( U(w) = U & F(x) = int[ f(x) ]d[x] ) ==>

Si I_{c} = int[ (r/s)^{2}·Ma·f(an) ]d[n] ==> 

I_{c} = (r/s)^{2}·M·F(an)

x(t) = (1/(md))·(r/s)^{2}·M·F(an)

w(t) = ( 2U )^{(1/2)}·(s/r)·( 1/(M·F(an)) )^{(1/2)}·t

K(t) = ( 2U )^{(1/2)}·(r/s)·( M·F(an) )^{(1/2)}

Ley:

Sea U(w) = U ==>

Si I_{c} = int[ (n/s)^{2}·Ma ]d[n] ==> 

I_{c} = (1/3)·(n/s)^{2}·Man

x(t) = (1/(md))·(1/3)·(n/s)^{2}·Man

w(t) = ( 6U )^{(1/2)}·(s/n)·( 1/(Man) )^{(1/2)}·t

K(t) = ( 6U )^{(1/2)}·(1/3)·(n/s)·( Man )^{(1/2)}

Ley:

Sea ( U(w) = U & F(x) = int[ f(x) ]d[x] & G(x) = int[ g(x) ]d[x] ) ==>

Si I_{c} = int-int[ (r/s)^{2}·Ma^{2}·f(ap)·g(aq) ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·F(ap)·G(aq)

x(t) = (1/(md))·(r/s)^{2}·M·F(ap)·G(aq)

w(t) = ( 2U )^{(1/2)}·(s/r)·( 1/(M·F(ap)·G(aq)) )^{(1/2)}·t

K(t) = ( 2U )^{(1/2)}·(r/s)·( M·F(an)·G(aq) )^{(1/2)}

Deducción:

I_{c} = int-int[ (r/s)^{2}·M·f(ap)·g(aq) ]d[ap]d[aq] = (r/s)^{2}·M·int-int[ f(ap)·g(aq) ]d[ap]d[aq] = ...

... (r/s)^{2}·M·int[ g(aq)·int[ f(ap) ]d[ap] ]d[aq] = (r/s)^{2}·M·int[ g(aq)·F(ap) ]d[aq] = ...

... (r/s)^{2}·M·F(ap)·int[ g(aq) ]d[aq] = (r/s)^{2}·M·F(ap)·G(aq)

Ley:

Sea ( U(w) = U & F(x) = int[ f(x) ]d[x] & G(x) = int[ g(x) ]d[x] ) ==>

Si I_{c} = int-int[ (r/s)^{2}·Ma^{2}·( f(ap)+g(aq) ) ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·( F(ap)·aq+ap·G(aq) )

x(t) = (1/(md))·(r/s)^{2}·M·( F(ap)·aq+ap·G(aq) )

w(t) = ( 2U )^{(1/2)}·(s/r)·( 1/(M·( F(ap)·aq+ap·G(aq) )) )^{(1/2)}·t

K(t) = ( 2U )^{(1/2)}·(r/s)·( M·( F(ap)·aq+ap·G(aq) ) )^{(1/2)}

Ley:

Sea ( U(w) = U & p = r·sin(nw) & q = r·cos(nw) ) ==>

Si I_{c} = int-int[ (1/2)·( (p/s)^{2}+(q/s)^{2} )·Ma^{2} ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·(1/4)·npi·(ar)^{2}

x(t) = (1/(md))·(r/s)^{2}·M·(1/4)·npi·(ar)^{2}

w(t) = ( (8/(npi))·U )^{(1/2)}·(s/r)·(1/(ar))·(1/M)^{(1/2)}·t

K(t) = ( (8/(npi))·U )^{(1/2)}·(r/s)·(ar)·M^{(1/2)}

Deducción:

d[p] = nr·cos(nw)·d[w] & d[q] = nr·(-1)·sin(nw)·d[w]

d[p]d[q] = (nr)^{2}·cos(nw)·(-1)·sin(nw)·d[w]d[w]

Ley:

Sea ( U(w) = U & p = (r/i)·sinh(nw) & q = r·cosh(nw) ) ==>

Si I_{c} = int-int[ (1/2)·( (p/s)^{2}+(q/s)^{2} )·Ma^{2} ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·(1/4)·npi·(ar)^{2}

Motores de rotación.

Ley:

Sea U(w) = U ==>

Si d[I_{c}] = (1/s)^{2}·Mrv·d[t] ==>

x(t) = (1/(md))·(1/s)^{2}·Mrvt

w(t) = ( (8/M)·(1/(rv))·U )^{(1/2)}·st^{(1/2)}

Ley:

Sea U(w) = U ==>

Si d[I_{c}] = (1/s)^{2}·Mrgt·d[t] ==>

x(t) = (1/(md))·(1/s)^{2}·Mrg·(1/2)·t^{2}

w(t) = ( (4/M)·(1/(rg))·U )^{(1/2)}·s·ln(ut)

Articulaciones robóticas y de vehículo.

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mv·d[x] ==>

x(t) = re^{(M/m)·(v/d)·(1/s)^{2}·t}

w(t) = ( (8/(mdr))·U )^{(1/2)}·(-1)·(m/M)·(d/v)·s^{2}·e^{(-1)·(1/2)·(M/m)·(v/d)·(1/s)^{2}·t}

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mg·d[tx] ==>

x(t) = re^{(M/m)·(g/d)·(1/s)^{2}·(1/2)·t^{2}}

w(t) = ( (8/(mdr))·U )^{(1/2)}·...

... ( (-1)·(m/M)·(d/g)·s^{2}·ln(ut) ) [o(t)o] e^{(-1)·(1/2)·(M/m)·(g/d)·(1/s)^{2}·(1/2)·t^{2}}

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mav·2x·d[x] ==>

x(t) = ( (-1)·(M/m)·(v/d)·(1/s)^{2}·at )^{(-1)}

w(t) = ( (2/(md))·U )^{(1/2)}·( (-1)·(M/m)·(v/d)·(1/s)^{2}·a )^{(1/2)}·(2/3)·t^{(3/2)}

Deducción:

d_{x}[ x^{2} ] = 2x

d_{x}[ x^{2} ]·d[x] = 2x·d[x]

d[ x^{2} ] = 2x·d[x]

L(t) = int[ d[L(t)] ] = int[ (1/s)^{2}·Mav·2x·d[x] ] = ...

... int[ (1/s)^{2}·Mav ]d[x^{2}] =  (1/s)^{2}·Mav·int[ d[x^{2}] ] =  (1/s)^{2}·Mavx^{2}

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mag·( d[t]·x^{2}+t·2x·d[x] ) ==>

x(t) = ( (-1)·(M/m)·(g/d)·(1/s)^{2}·a·(1/2)·t^{2} )^{(-1)}

w(t) = ( (2/(md))·U )^{(1/2)}·( (-1)·(M/m)·(g/d)·(1/s)^{2}·a·(1/2) )^{(1/2)}·(1/2)·t^{2}

Deducción:

d_{t}[ tx^{2} ] = d_{t}[t]·x^{2}+t·2x·d_{t}[x]

d_{t}[ tx^{2} ]·d[t] = ( d_{t}[t]·x^{2}+t·2x·d_{t}[x] )·d[t]

d[ tx^{2} ] = d[t]·x^{2}+t·2x·d[x]

L(t) = int[ d[L(t)] ] = int[ (1/s)^{2}·Mag·( d[t]·x^{2}+t·2x·d[x] ) ] = ...

... int[ (1/s)^{2}·Mag ]d[tx^{2}] =  (1/s)^{2}·Mag·int[ d[tx^{2}] ] =  (1/s)^{2}·Magtx^{2}

Ley: [ de rezo al Mal ]

Los hombres no están atacando,

a los xtraterrestres.

Los xtraterrestres no están atacando,

a los hombres.

Ley:

Se matan entre ellos en su mundo.

Cometen adulterio entre ellos en su mundo.

Principio:

U(x,y,z) = Potencial[ Q(x,y,z) ]

U(yz,zx,xy) = Anti-Potencial[ Q(yz,zx,xy) ]

Principio:

div-exp[ U(x,y,z) ] = sum[k = 1]-[3][ d_{xyz}^{3}[ e^{U_{k}(x,y,z)} ]

Si div-exp[ U(x,y,z) ] = 0 ==>

div-exp[ U(x,y,z) ] = d_{xyz}^{3}[ e^{sum[k = 1]-[3][ U_{k}(x,y,z) ]} ]

Principio:

Anti-div-exp[ U(yz,zx,xy) ] = sum[k = 1]-[3][ d_{kij}^{2}[ e^{U_{k}(yz,zx,xy)} ] ]

Si Anti-div-exp[ U(yz,zx,xy) ] = 0 ==>

Anti-div-exp[ U(yz,zx,xy) ] = d_{kij}^{2}[ e^{sum[k = 1]-[3][ U_{k}(yz,zx,xy) ]} ]

Ley:

Si Q(x,y,z) = U·< (1/x),(1/y),(1/z) > ==> 

U(x,y,z) = U·( ln(ax)+ln(ay)+ln(az) )

div-exp[ U(x,y,z) ] = Ua^{3}

F(z) = int-int[ div-exp[ U(x,y,z) ] ]d[x]d[x]+int-int[ div-exp[ U(x,y,z) ] ]d[y]d[y] = ...

... Ua^{3}·(1/2)·( x^{2}+y^{2} )

Ley:

Si Q(yz,zx,xy) = U·< (1/(yz)),(1/(zx)),(1/(xy)) > ==> 

U(yz,zx,xy) = U·( ln(byz)+ln(bzx)+ln(bxy) )

Anti-div-exp[ U(yz,zx,xy) ] = Ub^{3}·4xyz

F(z) = int-int[ Anti-div-exp[ U(yz,zx,xy) ] ]d[x]d[y]+int-int[ Anti-div-exp[ U(yz,zx,xy) ] ]d[y]d[x] = ...

... Ub^{3}·2z·(xy)^{2}

Ley:

Si Q(x,y,z) = aU·< ((y+z)/x),((z+x)/y),((x+y)/z) > ==> 

U(x,y,z) = U·( (ay+az)·ln(ax)+(az+ax)·ln(ay)+(ax+ay)·ln(az) )

div-exp[ U(x,y,z) ] = Ua^{3}·( ...

... (ax)^{ay+az+(-1)}·ln(ax)·( 2+(ay+az)·ln(ax) )+...

... (ay)^{az+ax+(-1)}·ln(ay)·( 2+(az+ax)·ln(ay) )+...

... (az)^{ax+ay+(-1)}·ln(az)·( 2+(ax+ay)·ln(az) ) )

Ley:

E(x_{k}) = int-int[ div-exp[ U_{k}(x,y,z) ] ]d[(1/a)^{2}·(i+j)] = ...

... U·(ak)^{ai+aj+(-1)}·[o(ai+aj)o] ( 2+(1/2)·(ai+aj)·ln(ak) )·(ai+aj)

x_{k}(t) = ...

... (1/a)·Anti-[ ( s /o(s)o/ ...

... int[ (as)^{ai+aj+(-1)}·[o(ai+aj)o] ( 2+(1/2)·(ai+aj)·ln(as) )·(ai+aj) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/m)·U )^{(1/2)}·at )

Deducción:

d_{ax}[ (ax)^{ay+az} ] = (ay+az)·(ax)^{ay+az+(-1)} 

d_{ay}[ (ay+az)·(ax)^{ay+az+(-1)} ] = (ax)^{ay+az+(-1)}·( 1+ay·ln(ax)+az·ln(ax) )

d_{az}[ (ax)^{ay+az+(-1)}·( 1+(ay+az)·ln(ax) ) ] = (ax)^{ay+az+(-1)}·ln(ax)·( 2+(ay+az)·ln(ax) )

Ley:

Si Q(yz,zx,xy) = bU·< ((zx+xy)/(yz)),((xy+yz)/(zx)),((yz+zx)/(xy)) > ==> 

U(yz,zx,xy) = U·( (bzx+bxy)·ln(byz)+(bxy+byz)·ln(bzx)+(byz+bzx)·ln(bxy) )

Anti-div-exp[ U(yz,zx,xy) ] = Ub·( ...

... (byz)^{bzx+bxy+(-1)}·(bz+by)·( 1+ln(byz) )+...

... (bzx)^{bxy+byz+(-1)}·(bx+bz)·( 1+ln(bzx) )+...

... (bxy)^{byz+bzx+(-1)}·(by+bx)·( 1+ln(bxy) ) )

Ley:

E(x_{k}) = int[ Anti-div-exp[ U_{k}(yz,zx,xy) ] ]d[(1/b)·k] = U·(bij)^{bik+bkj+(-1)}·( ( 1/ln(bij) )+1 )

x_{k}(t) = (a/b)·Anti-[ ( s /o(s)o/ int[ (bij)^{ais+asj+(-1)}·( ( 1/ln(bij) )+1 ) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/m)·U )^{(1/2)}·(b/a)·t )

Deducción:

d_{byz}[ (byz)^{bzx+bxy} ] = (bzx+bxy)·(byz)^{bzx+bxy+(-1)}

d_{x}[ (bzx+bxy)·(byz)^{bzx+bxy+(-1)} ] = (byz)^{bzx+bxy+(-1)}·(bz+by)·( 1+ln(byz) )

Áreas y Volumenes:

Teorema:

x = r·cos(w)

y = r·sin(w)

d[x]d[y] = (1/2)·( d[x]d[y]+d[x]d[y] ) = ...

... (1/2)·( d_{r}[x]·d_{w}[y]+(-1)·d_{w}[x]·d_{r}d[y] )·d[r]d[w]

Teorema:

Área de un círculo:

A(r) = int[w = 0]-[2pi][ inr[r = 0]-[r][ r ]d[r] ]d[w] = ...

... int[w = 0]-[2pi][ (1/2)·r^{2} ]d[w] = (1/2)·r^{2}·int[w = 0]-[2pi][ d[w] ] = pi·r^{2}

Perímetro de un círculo:

B(r) = d_{r}[ A(r) ] = d_{r}[ pi·r^{2} ] = 2pi·r

Teorema:

Área de un sector circular:

A(r,w) = int[w = 0]-[w][ inr[r = 0]-[r][ r ]d[r] ]d[w] = ...

... int[w = 0]-[w][ (1/2)·r^{2} ]d[w] = (1/2)·r^{2}·int[w = 0]-[w][ d[w] ] = (1/2)·wr^{2}

Perímetro de un sector circular:

B(r,w) = d_{r}[ A(r,w) ] = d_{r}[ (1/2)·wr^{2} ] = wr

Teorema:

d[z] = r·sin(s)·d[s]

x = r·cos(2w)

y = r·sin(2w)

d[x]d[y]d[z] = (1/2)·( d[x]d[y]d[z]+d[x]d[y]d[z] ) = ...

... (1/2)·( d_{r}[x]·d_{w}[y]+(-1)·d_{w}[x]·d_{r}d[y] )·r·sin(s)·d[r]d[w]d[s] = 

Teorema:

Volumen de una esfera:

A(r) = int[s = 0]-[pi][ int[w = 0]-[2pi][ int[r = 0]-[r][ r^{2}·sin(s) ]d[r] ]d[w] ]d[s] = ...

... int[s = 0]-[pi][ int[w = 0]-[2pi][ (1/3)·r^{3}·sin(s) ]d[w] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·int[w = 0]-[2pi][ d[w] ] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·2pi ]d[s] = (2/3)·pi·r^{3}·int[s = 0]-[pi][ sin(s) ]d[s] = ...

... (2/3)·pi·r^{3}·(-1)·( cos(pi)+(-1)·cos(0) ) = (4/3)·pi·r^{3}

Superficie de una esfera:

B(r) = d_{r}[ A(r) ] = d_{r}[ (4/3)·pi·r^{3} ] = 4pi·r^{2}

Teorema:

Volumen de un hemisferio:

A(r,w) = int[s = 0]-[pi][ int[w = 0]-[w][ int[r = 0]-[r][ r^{2}·sin(s) ]d[r] ]d[w] ]d[s] = ...

... int[s = 0]-[pi][ int[w = 0]-[w][ (1/3)·r^{3}·sin(s) ]d[w] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·int[w = 0]-[w][ d[w] ] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·w ]d[s] = (2/3)·wr^{3}·int[s = 0]-[pi][ sin(s) ]d[s] = ...

... (2/3)·wr^{3}·(-1)·( cos(pi)+(-1)·cos(0) ) = (2/3)·wr^{3}

Superficie de un hemisferio:

B(r,w) = d_{r}[ A(r,w) ] = d_{r}[ (2/3)·wr^{3} ] = 2wr^{2}

--------------------------------

Mecánica Teórica y Ondas:

--------------------------------

Teorema:

Sea d_{x}[F(x)] = f(x) ==>

d_{x}[ Anti-[F(s)]-(x) ] = ( 1/f( Anti-[F(s)]-(x) ) )

Demostración:

d_{y}[ Anti-[F(s)]-( F(y) ) ] = d_{y}[y] = 1

d[ Anti-[F(s)]-( F(y) ) ] = d[y]

d_{F(y)}[ Anti-[F(s)]-( F(y) ) ] = d_{F(y)}[y] = ( 1/d_{y}[F(y)]) = ( 1/f(y) )

Sea y = Anti-[F(s)]-(x) ==>

d_{F( Anti-[F(s)]-(x) )}[ Anti-[F(s)]-( F( Anti-[F(s)]-(x) ) ) ] = ( 1/f( Anti-[F(s)]-(x) ) )

Teorema:

Sea d_{x}[F(x)] = f(x) ==>

d_{x}[ Anti-[( s /o(s)o/ F(s) )]-(x) ] = f( Anti-[( s /o(s)o/ F(s) )]-(x) )

Demostración:

d_{x}[ Anti-[( s /o(s)o/ F(s) )]-(x) ] = ( 1/( 1/f( Anti-[( s /o(s)o/ F(s) )]-(x) ) ) ) = ...

... f( Anti-[( s /o(s)o/ F(s) )]-(x) )

Teorema:

d_{x}[ arc-sin(x) ] = ( 1/(1+(-1)·x^{2})^{(1/2)} )

Demostración:

d_{x}[ arc-sin(x) ] = ( 1/cos( arc-sin(x) ) ) = ( 1/(1+(-1)·(sin( arc-sin(x) ))^{2})^{(1/2)} )

Teorema:

d_{x}[ arc-cos(x) ] = (-1)·( 1/(1+(-1)·x^{2})^{(1/2)} )

Demostración:

d_{x}[ arc-cos(x) ] = (-1)·( 1/sin( arc-cos(x) ) ) = ( 1/(1+(-1)·(cos( arc-cos(x) ))^{2})^{(1/2)} )

Racionamiento antiguo:

Teorema:

d_{x}[ e^{x} ] = e^{x}

Demostración:

d_{x}[ e^{x} ] = ( 1/(1/y) ) = y = e^{x}

Teorema:

d_{x}[ ln(x) ] = (1/x)

Demostración:

d_{x}[ ln(x) ] = ( 1/e^{y} ) = ( 1/e^{ln(x)} ) = (1/x)

Teorema:

Sea x(t) = Anti-[ ( s /o(s)o/ int[ F(s) ]d[s] )^{[o(s)o] (1/2)} ]-( 2^{(1/2)}·ut ) ] ==>

(1/2)·d_{t}[x(t)]^{2} = F(s)·u^{2}

d_{tt}^{2}[x(t)] = (1/2)·( F(s) )^{(-1)·(1/2)}·f(s)·( F(s) )^{(1/2)}·2u^{2} = f(s)·u^{2}

Demostración:

d_{t}[ F(s) ] = d_{s}[F(s)]·d_{t}[s]

Teorema:

Sea x(t) = Anti-[ ( s /o(s)o/ int[ H(ut) [o(ut)o] F(s) ]d[s] )^{[o(s)o] (1/2)} ]-( 2^{(1/2)}·ut ) ] ==>

(1/2)·d_{t}[x(t)]^{2} = ( H(ut) [o(ut)o] F(s) )·u^{2}

d_{tt}^{2}[x(t)] = ...

... (1/2)·( H(ut) [o(ut)o] F(s) )^{(-1)·(1/2)}·h(ut)·f(s)·( H(ut) [o(ut)o] F(s) )^{(1/2)}·2u^{2} = ...  

... h(ut)·f(s)·u^{2}

Demostración:

u·d_{ut}[ H(ut) [o(ut)o] F(s) ] = u·d_{ut}[H(ut)]·d_{ut}[F(s)] = ...

... u·h(ut)·d_{s}[F(s)]·d_{ut}[s] = h(ut)·d_{s}[F(s)]·d_{t}[s]

Teorema:

Sea x(t) = Anti-[ ( s /o(s)o/ int[ (ut) [o(ut)o] F(s) ]d[s] )^{[o(s)o] (1/2)} ]-( 2^{(1/2)}·ut ) ] ==>

(1/2)·d_{t}[x(t)]^{2} = ( (ut) [o(ut)o] F(s) )·u^{2}

d_{tt}^{2}[x(t)] = ...

... (1/2)·( (ut) [o(ut)o] F(s) )^{(-1)·(1/2)}·f(s)·( (ut) [o(ut)o] F(s) )^{(1/2)}·2u^{2} = f(s)·u^{2}

Ley:

d[H(t)] = (1/pi)^{2}·MgI·d[tx]

x(t) = (1/a)·Anti-[ ( s /o(s)o/ int[ (1/2)·(ut)^{2} [o(ut)o] (1/2)·s^{2} ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( 2·(M/m)·gI·(1/u)·(1/d) )^{(1/2)}·(1/pi)·t )

Deducción:

H(t) = int[ d[H(t)] ] = int[ (1/pi)^{2}·MgI ]d[tx] = (1/pi)^{2}·MgI·int[ d[tx] ] = (1/pi)^{2}·MgItx

md·d_{tt}^{2}[x] = (1/pi)^{2}·MgItx

md·d_{tt}^{2}[x]·d[x] = (1/pi)^{2}·MgI·(1/u)·(ut)·x·d_{ut}[x]·d[ut]

md·(1/2)·d_{t}[ax]^{2} = (1/pi)^{2}·MgI·(1/u)·(1/2)·(ut)^{2} [o(ut)o] (1/2)·(ax)^{2}

Ley:

d[H(t)] = (1/pi)^{2}·Mv·d[(1/t)·x]

x(t) = (1/a)·Anti-[ ( s /o(s)o/ int[ ln(ut) [o(ut)o] (1/2)·s^{2} ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( 2·(M/m)·(vu)·(1/d) )^{(1/2)}·(1/pi)·t )

Deducción:

H(t) = int[ d[H(t)] ] = int[ (1/pi)^{2}·Mv ]d[(1/t)·x] = (1/pi)^{2}·Mv·int[ d[(1/t)·x] ] = ...

... (1/pi)^{2}·Mv·(1/t)·x

md·d_{tt}^{2}[x] = (1/pi)^{2}·Mv·(1/t)·x

md·d_{tt}^{2}[x]·d[x] = (1/pi)^{2}·Mvu·(1/(ut))·x·d_{ut}[x]·d[ut]

md·(1/2)·d_{t}[ax]^{2} = (1/pi)^{2}·Mvu·ln(ut) [o(ut)o] (1/2)·(ax)^{2}

Ley:

Le tenéis que decir a Esquerra Republicana,

que queréis el título de la universidad de Stroniken como el mío,

enseñando el testimonio de uno mismo con Dios,

escrito con vuestra letra:

Jûan Garriga Peralta-Peraltotzak:

Filósofo de la ciencia matemática y de la ciencia lógica,

por la universidad de Stroniken.

Y que vos lo envíen.

Ley: [ de onda electro-magnética plana de superficie ]

Lap[ E_{e}(x,y,t) ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ int[ B_{e}(x,y,t) ]d[t] ]

Deducción:

E_{e}(x,y,t)+int[ B_{e}(x,y,t) ]d[t] = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·cos(w) 

y(t) = ct·sin(w)

Lap[ int[ B_{e}(x,y,t) ]d[t] ] = ...

... ( 1/(d[x]^{2}+d[y]^{2}) )·(d[x]^{2}+d[y]^{2}) [o] Lap[ int[ B_{e}(x,y,t) ]d[t] ]

Lap[ E_{e}(x,y,t) ]+Lap[ int[ B_{e}(x,y,t) ]d[t] ]= 0^{3}

Lap[ E_{e}(x,y,t) ]+2·(1/c)^{2}·d_{tt}^{2}[ int[ B_{e}(x,y,t) ]d[t] ] = 0^{3}

Lap[ E_{e}(x,y,t) ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ int[ B_{e}(x,y,t) ]d[t] ]

Ley: [ de onda gravito-magnética plana de superficie ]

Lap[ int[ B_{g}(x,y,t) ]d[t] ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ E_{g}(x,y,t) ]

Deducción:

int[ B_{g}(x,y,t) ]d[t]+E_{g}(x,y,t) = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·cos(w) 

y(t) = ct·sin(w)

Lap[ E_{g}(x,y,t) ] = ( 1/(d[x]^{2}+d[y]^{2}) )·(d[x]^{2}+d[y]^{2}) [o] Lap[ E_{g}(x,y,t) ]

Lap[ int[ B_{g}(x,y,t) ]d[t] ]+Lap[ E_{g}(x,y,t) ] = 0^{3}

Lap[ int[ B_{g}(x,y,t) ]d[t] ]+2·(1/c)^{2}·d_{tt}^{2}[ E_{g}(x,y,t) ] = 0^{3}

Lap[ int[ B_{g}(x,y,t) ]d[t] ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ E_{g}(x,y,t) ]

Ecuaciones de ondas elípticas planas de superficie:

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = (1/2)·( ...

... e^{ax+ay+acit || ln( H(ax,ay) )+act}+...

... e^{ax+ay+acit || ln( H(ax,ay) )+(-1)·act} )

u(x,y,0) = H(ax,ay)

d_{t}[ u(x,y,0) ] = 0

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·(1/2)·act·0 || (2t)^{(1/2)}]-[h(ax,ay)+(1/2)·act·0 || (2t)^{(1/2)}][ w ]d[w] ]·...

... e^{ax+ay+acit || 0}

u(x,y,0) = 0

d_{t}[ u(x,y,0) ] = ac·h(ax,ay)

Ecuaciones de ondas hiperbólicas planas de superficie:

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = (1/2)·( ...

... e^{ax+ay+act || ln( H(ax,ay) )+act}+...

... e^{ax+ay+act || ln( H(ax,ay) )+(-1)·act} )

u(x,y,0) = H(ax,ay)

d_{t}[ u(x,y,0) ] = 0

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·(1/2)·act·0 || (2t)^{(1/2)}]-[h(ax,ay)+(1/2)·act·0 || (2t)^{(1/2)}][ w ]d[w] ]·...

... e^{ax+ay+act || 0}

u(x,y,0) = 0

d_{t}[ u(x,y,0) ] = ac·h(ax,ay)

Ley:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = E_{e}·(1/2)·( ...

... e^{ax+ay+acit || ln( (ax)^{2}+(ay)^{2} )+act}+...

... e^{ax+ay+acit || ln( (ax)^{2}+(ay)^{2} )+(-1)·act} )

u(x,y,0) = (ax)^{2}+(ay)^{2}

d_{t}[ u(x,y,0) ] = 0

Ley:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = E_{e}·sum[k = 1]-[oo][ ...

... int[(ax+ay)+(-1)·act·0 || (2t)^{(1/2)}]-[(ax+ay)+act·0 || (2t)^{(1/2)}][ w ]d[w] ]·...

... e^{ax+ay+acit || 0}

u(x,y,0) = 0

d_{t}[ u(x,y,0) ] = 2ac·(ax+ay)

producto-tensorial y teoría-de-juegos-en-economía-y-física y análisis-matemático-5 y mecánica-momento-de-inercia

Teorema:

A = k·( < a,0 > % < 0,a >)

B = k·( < a,0 > % < 0,(-a) >)

dim(A) = (1/2)

dim(B) = (1/2)

( < a,0 > % < 0,0 >) = (1/2)·( < a,0 > % < 0,a >)+(1/2)·( < a,0 > % < 0,(-a) >)

Lema: [ de gasto en defensa ]

PIB por cápita 8,400€

inversión del 5%:

(1/20)·32,000+20·1,600 = 33,600€ por cada 4 catalanohablantes.

Compra de armamento de 32,700€ por pack militar:

misil o torpedo o caja de proyectiles de cañón.

Lema:

Estrategia ganadora de venta,

del supremo o igual:

Make America empate again.

h(1) = 32,700€

F(1,1) = 1·1+(1+1) = 3

Estrategia ganadora de no venta,

del ínfimo o igual:

Make America first again.

h(2) = 65,400€

F(2,0) = 2·0+(2+0) = 2

Estrategias perdedoras:

h(1/2) = 16,350€

h(3/2) = 49,050€

F((1/2),(3/2)) = (3/4)+((1/2)+(3/2)) = (2.75)

F((3/2),(1/2)) = (3/4)+((3/2)+(1/2)) = (2.75)

Ley:

Hay gente que no es,

que no hay condenación.

Hay gente que es,

que hay condenación.

Deducción: [ por teoría de juegos ]

Jugadas ganadoras:

Joder a un esclavo infiel:

F(1,(-1)) = (-1)+(1+(-1)) = (-1)

F(2,(-1)) = (-2)+(2+(-1)) = (-1)

Jugadas perdedoras:

Joder a un señor fiel:

F(1,(-2)) = (-2)+(1+(-2)) = (-3)

F(2,(-2)) = (-4)+(2+(-2)) = (-4)

Ley:

Solo se puede conquistar con victoria,

haciendo que los infieles del Gestalt ignoren a los señores.

Solo se puede liberar con victoria,

no haciendo que los fieles del Gestalt ignoren a los señores.

Deducción: [ por teoría de juegos ]

Jugada ganadora:

Ignorar los infieles del Gestalt a los señores:

F(0,(-1)) = 0+(0+(-1)) = (-1)

Los infieles joden a infieles.

Jugada perdedora:

Ignorar los fieles del Gestalt a los señores:

F(0,(-2)) = 0+(0+(-2)) = (-2)

Los infieles joden a fieles.

Dual por dual de sabor:

Basik-kowetch-tate oil.

Acid-kowetch-tate wine.

Teorema:

int[x = 0]-[ln(oo)][ e^{(-1)·x^{n}} ]d[x] = (1/n!)

Teorema:

int[x = 0]-[ln(oo^{m+1})][ x^{m}·e^{(-x)} ]d[x] = m!

int[x = 0]-[ln(oo^{m+1})][ x^{m}·e^{(-1)·x^{n}} ]d[x] = (m!/n!)

Teorema:

int[x = 0]-[ln(oo^{(1/m)+1})][ x^{(1/m)}·e^{(-x)} ]d[x] = m

int[x = 0]-[ln(oo^{(1/m)+1})][ x^{(1/m)}·e^{(-1)·x^{n}} ]d[x] = m·( m!/(mn)! )

Demostración:

m = 0 & n = 1

int[x = 0]-[ln(oo)][ e^{(-1)·x} ]d[x] = [ (-1)·e^{(-1)·x} ]_{x = 0}^{x = ln(oo)} = 1

m = 1 & n = 1

int[x = 0]-[ln(oo^{2})][ xe^{(-1)·x} ]d[x] = ...

... [ (-1)·xe^{(-1)·x} ]_{x = 0}^{x = ln(oo^{2})}+[ (-1)·e^{(-1)·x} ]_{x = 0}^{x = ln(oo)} = 1

Teorema:

ln( (p+1)^{oo} ) = ( oo·log_{p+1}(2^{p}) )·ln(p+1) = ln(2^{p})·oo = ln(oo^{p})

Arte:

[En][ int[x = 0]-[ln(oo)][ e^{(-1)·x^{n}} ]d[x] = (1/n) ]

Exposición:

n = 1

Se define H(t) = int[x = 0]-[ln(oo)][ e^{(-1)·x^{n}·F(t)} ]d[x] ==>

d_{t}[H(t)] = f(t)·int[x = 0]-[ln(oo)][ (-1)·x^{n}·e^{(-1)·x^{n}·F(t)} ]d[x]

F(t) = x

d_{t}[H(t)] = d_{t}[x]·( 1/(n+1) )·(-1)

H(t) = x·( 1/(n+1) )·(-1) = F(t)·( 1/(n+1) )·(-1)

H( F^{o(-1)}(1) ) = F( F^{o(-1)}(1) )·( 1/(n+1) )·(-1) = ( 1/(n+1) )·(-1)

u(1) = (1/n)

v(1/n) = 0

H( F^{o(-1)}(1) ) = ( 1/(n+u(1)) )·(-1)^{u(1)} = ( 1/(n+v(1/n)) )·(-1)^{v(1/n)} = (1/n)

Arte:

[En][Em][ int[x = 0]-[ln(oo^{m+1})][ x^{m}·e^{(-1)·x^{n}} ]d[x] = ( 1/(m+n) ) ]

Exposición:

m = 0 & n = 1

Se define H(t) = int[x = 0]-[ln(oo^{m+1})][ x^{m}·e^{(-1)·x^{n}·F(t)} ]d[x] ==>

d_{t}[H(t)] = f(t)·int[x = 0]-[ln(oo^{m+1})][ (-1)·x^{m+n}·e^{(-1)·x^{n}·F(t)} ]d[x]

F(t) = x^{m+1}

d_{t}[H(t)] = (m+1)·x^{m}·d_{t}[x]·( 1/(m+n+1) )·(-1)

H(t) = x^{m+1}·( 1/(m+n+1) )·(-1) = F(t)·( 1/(m+n+1) )·(-1)

H( F^{o(-1)}(1) ) = F( F^{o(-1)}(1) )·( 1/(m+n+1) )·(-1) = ( 1/(m+n+1) )·(-1)

u(1) = (1/n)

v(1/n) = 0

H( F^{o(-1)}(1) ) = ( 1/(m+n+u(1)) )·(-1)^{u(1)} = ( 1/(m+n+v(1/n)) )·(-1)^{v(1/n)} = ( 1/(m+n) )

Teorema:

int[x = 0]-[oo][ ( sin(nx)/(nx) ) ]d[x] = (pi/n)

Demostración:

Se define H(t) = int[x = 0]-[oo][ e^{(-1)·(nxt)}·( sin(nx)/(nx) ) ]d[x] ==>

y = nx & d[y] = n·d[x]

H(t) = (1/n)·int[y = 0]-[oo][ e^{(-1)·(yt)}·( sin(y)/y ) ]d[y]

d_{t}[H(t)] = (-1)·(1/n)·int[y = 0]-[oo][ e^{(-1)·(yt)}·sin(y) ]d[y]

d_{t}[H(t)] = (-1)·(1/n)·( 1/(t^{2}+1) )

H(t) = (-1)·(1/n)·arc-tan(t)

H(0) = (-1)·(1/n)·(-pi) = (pi/n)

Teorema:

int[x = 0]-[oo][ ( cos(x/n)/x ) ]d[x] = ln(n)

Demostración:

Se define H(t) = int[x = 0]-[oo][ e^{(-1)·(xt)}·( cos(x/n)/x ) ]d[x] ==>

H(t) = int[x = 0]-[oo][ e^{(-1)·(xt)}·( cos(x/n)/x ) ]d[x]

d_{t}[H(t)] = (-1)·int[x = 0]-[oo][ e^{(-1)·(xt)}·cos(x/n) ]d[x]

d_{t}[H(t)] = (-1)·( t/(t^{2}+(1/n)^{2}) )

H(t) = (-1)·(1/2)·ln(t^{2}+(1/n)^{2})

H(0) = (-1)·(1/2)·2·ln(1/n) = ln(n)

Teorema:

int[x = ln(0)]-[0][ int[y = ln(0)]-[0][ e^{(-1)·( x^{n}+y^{n} )} ]d[y] ]d[x] = (1/n!)^{2}

Demostración:

e^{(-1)·( x^{n}+y^{n} )} [o(x || y)o] ( x /o(x || y)o/ x^{n} ) [o(x || y)o] ( y /o(x || y)o/ y^{n} )

Teorema:

int[x = 0]-[ln(oo)][ e^{(-1)·x^{2}} ]d[x] = (1/2!)

Demostración:

int[w = 0]-[2pi][ int[r = 0]-[oo][ e^{(-1)·r^{2}}·(1/4)·2r ]d[r] ]d[w] = (pi/2)

(-1)·e^{(-1)·r^{2}}·(1/4)·w = (-1)·e^{(-1)·( x^{2}+y^{2} )}·(1/4)·arc-tan(x/y)

arc-tan(0/oo)+(-1)·arc-tan(0/(-oo)) = 2pi

arc-tan(oo/(-oo)) = arc-tan(oo·(-0)) = arc-tan(oo·0) = arc-tan(oo/oo)

e^{(-1)·( x^{2}+y^{2} )}·(1/4)·8pi = (pi/2)

4 veces el cuadrante de la exponencial y valores convergentes de arco-tangente.

Teorema:

int[x = 0]-[pi][ e^{(-1)·( sin(x) )^{n}} ]d[x] = (2/n!)

Demostración:

int[x = 0]-[pi][ e^{(-1)·( sin(x) )^{n}}·( 1/d_{x}[sin(x)] ) ]d[sin(x)] = ...

... (-1)·e^{(-1)·( sin(x) )^{n}} [o(sin(x))o] ( sin(x) /o(sin(x))o/ ( sin(x) )^{n} )·( 1/cos(x) )

Teorema:

int[x = (-1)·(pi/2)]-[(pi/2)][ e^{(-1)·( cos(x) )^{n}} ]d[x] = (2/n!)

Demostración:

int[x = (-1)·(pi/2)]-[(pi/2)][ e^{(-1)·( cos(x) )^{n}}·( 1/d_{x}[cos(x)] ) ]d[cos(x)] = ...

... e^{(-1)·( cos(x) )^{n}} [o(cos(x))o] ( cos(x) /o(cos(x))o/ ( cos(x) )^{n} )·( 1/sin(x) )

Teorema:

int[x = (-oo)]-[oo][ ln(x^{n}+1) ]d[x] = n·( ln(2)+pi·i )

Área positiva > 1 + Área negativa < 1 = a la integral impropia

Verificación del método de Euler por Hôpital-Garriga:

( ln(x^{n}+1)+(-1) )·(x^{n}+1) [o(x)o] ( x /o(x)o/ (x^{n}+1) ) = ...

( ln(x^{n}+1)+(-1) )·(w^{n}+1) [o(x)o] ( w /o(x)o/ (w^{n}+1) ) = ...

( ln(x^{n}+1)+(-1) ) [o(x)o] ( 1 /o(x)o/ 1 ) = [ ln(x^{n}+1)+(-1) ]_{x = (-oo)}^{x = oo}

Demostración:

Se define H(t) = int[x = (-oo)]-[oo][ ln( (xF(t))^{n}+1 ) ]d[x] ==>

d_{t}[H(t)] = f(t)·int[x = (-oo)]-[oo][ ( 1/( (xF(t))^{n}+1 ) )·n·( xF(t) )^{n+(-1)}·x ]d[x]

F(t) = x

d_{t}[H(t)] = d_{t}[x]·int[x = (-oo)]-[oo][ ( 1/(x^{2n}+1) )·nx^{2n+(-1)} ]d[x]

d_{t}[H(t)] = d_{t}[x]·(1/2)·( ln(oo^{2n}+1) )+(-1)·ln((-oo)^{2n}+1) )

d_{t}[H(t)] = d_{t}[x]·(1/2)·2n·( ln(oo)+(-1)·ln(oo)+pi·i ) = d_{t}[x]·n·( ln(2)+pi·i )

H(t) = x·n·( ln(2)+pi·i ) = F(t)·n·( ln(2)+pi·i )

H( F^{o(-1)}(1) ) = F( F^{o(-1)}(1) ) n·( ln(2)+pi·i ) = n·( ln(2)+pi·i )

Arte:

[En][ int[x = (-1)]-[1][ ( 1/(x^{n}+(-1)) ) ]d[x] = (2/n) ]

Exposición:

n = 0

Se define H(t) = int[x = (-1)]-[1][ ( 1/( (xF(t))^{n}+(-1) ) ) ]d[x] ==>

d_{t}[H(t)] = f(t)·int[x = (-1)]-[1][ (-1)·( 1/( (xF(t))^{n}+(-1) ) )^{2}·n·( xF(t) )^{n+(-1)}·x ]d[x]

F(t) = x

d_{t}[H(t)] = d_{t}[x]·int[x = (-1)]-[1][ (-1)·( 1/(x^{2n}+(-1)) )^{2}·nx^{2n+(-1)} ]d[x]

d_{t}[H(t)] = d_{t}[x]·(1/2)·( oo+(-oo) ) = d_{t}[x]·(1/2)

H(t) = x·(1/2) = F(t)·(1/2)

u(1) = m

v(m) = (4/n)

H( F^{o(-1)}(1) ) = F( F^{o(-1)}(1) )·(1/2) = (1/2)·u(1) = (1/2)·v(m) = (2/n)

Momento de inercia Wronskiano:

Ley:

Sea ( x = a·cos(ut) & y = b·sin(ut) ) ==>

M·int[ x·d_{t}[y]+(-y)·d_{t}[x] ]d[t] = M·ab·(ut)

Ley:

M·ab·(ut)·(1/2)·d_{t}[w]^{2} = E·H(w)

w(t) = Anti-[ ( int[ (ut) ]d[s] /o(s)o/ int[ H(s) ]d[s] )^{[o(s)o] (1/2)} ]-( ( (2/M)·(1/(ab) )·E )^{(1/2)}·t )

Ley:

Sea ( x = vt & y = g·(1/2)·t^{2} ) ==>

M·int[ x·d_{t}[y]+(-y)·d_{t}[x] ]d[t] = M·vg·(1/u)^{3}·(1/6)·(ut)^{3}

Ley:

M·vg·(1/u)^{3}·(ut)^{3}·(1/12)·d_{t}[w]^{2} = E·H(w)

w(t) = Anti-[ ( int[ (ut)^{3} ]d[s] /o(s)o/ int[ H(s) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (12/M)·(1/(vg) )·u^{3}·E )^{(1/2)}·t )

Ley:

Sea ( x = vt & y = re^{ut+(-1)} ) ==>

M·int[ x·d_{t}[y]+(-y)·d_{t}[x] ]d[t] = M·vr·(1/u)·(ut+(-1))^{2}·er-h[2]( ut+(-1) )

Ley:

M·vr·(1/u)·(ut+(-1))^{2}·er-h[2]( ut+(-1) )·(1/2)·d_{t}[w]^{2} = E·H(w)

w(t) = Anti-[ ( int[ (ut+(-1))^{2}·er-h[2]( ut+(-1) ) ]d[s] /o(s)o/ int[ H(s) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/M)·(1/(vr) )·uE )^{(1/2)}·t )

Ley:

Sea ( x = r·ln(ut) & y = vt ) ==>

M·int[ x·d_{t}[y]+(-y)·d_{t}[x] ]d[t] = M·vr·(1/u)·(ut)·( ln(ut)+(-2) )

Ley:

M·vr·(1/u)·(ut)·( ln(ut)+(-2) )·(1/2)·d_{t}[w]^{2} = E·H(w)

w(t) = Anti-[ ( int[ (ut)·( ln(ut)+(-2) ) ]d[s] /o(s)o/ int[ H(s) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/M)·(1/(vr) )·uE )^{(1/2)}·t )

Ley:

Sea d_{t}[x] = ru·(ut+e)^{sin(ut+(pi/2))} ==>

d_{tt}^{2}[x] = ru^{2}·(ut+e)^{sin(ut+(pi/2))}·( cos(ut+(pi/2))·ln(ut+e)+sin(ut+(pi/2))·(1/(ut+e)) )

x(t) = r·(ut+e)^{sin(ut+(pi/2))} [o(ut)o] ( ut /o(ut)o/ sin(ut+(pi/2))·ln(ut+e) )

x(0/u) = re

d_{t}[x(0/u)] = rue

d_{tt}^{2}[x(0/u)] = ru^{2}

Deducción:

ln(f(z)) = ln(g(z)^{h(z)}) = h(z)·ln(g(z))

d_{z}[f(z)] = f(z)·d_{z}[ h(z)·ln(g(z)) ]

Ley:

La verdad implica la felicidad.

La falsedad implica el sufrimiento.

Deducción:

Creer-se una verdad es jugada ganadora:

F(n,1) = n·1+(n+1) = 2n+1

Creer-se una falsedad es jugada perdedora:

F(n,0) = n·0+(n+0) = n

n [< n+n = 2n < 2n+1

Ley:

Un heterosexual que es,

no puede ser homosexual que no es.

Un homosexual que no es,

no puede ser heterosexual que es.

I havere-kate-kute maket-tikaletch-tuted a coment saksahuaketch-kán,

of yu tenotitch-lán.

Yu havere-kate-kute maket-tikaletch-tuted a coment saksahuaketch-kán,

of me tenotitch-lán.

El American-Quetchua tiene 7 dialectos:

Centro americano:

-tikaletch-kal

Sur americano hawsnutch:

-tikaletch-tate

-tikaletch-tute

-tikalet-kazhe

-tikalet-kuzhe

gwzenen plana

-tikalet-huw

yuhened plana

-tikalet-shuw

yushened plana

Ley:

Sea I_{c}·(1/2)·d_{t}[w]^{2} = E·H(w) ==>

Si d[ d[I_{c}] ] = Mrv·d[w]d[t] ==>

w(t) = Anti-[ ( ( (1/2)·s^{2} [o(s)o] int[ (ut) ]d[s] ) /o(s)o/ int[ H(s) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/M)·(1/(rv))·uE )^{(1/2)}·t )

Ley:

Sea I_{c}·(1/2)·d_{t}[w]^{2} = E·H(w) ==>

Si d[ d[I_{c}] ] = Mrgt·d[w]d[t] ==>

w(t) = Anti-[ ( ( (1/2)·s^{2} [o(s)o] int[ (ut)^{2} ]d[s] ) /o(s)o/ int[ H(s) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (4/M)·(1/(rg))·E )^{(1/2)}·ut )

Euskera-Bascotzok-ejército y integrales-de-la-física-matemática y economía-aranceles y productos-conectivos y evangelio-stronikiano

Ley:

Ibai sakona zeharkatzen-sua,

és-de-tek arriskatzi-ten-dut-zatu-dut.

Ibai azalea zeharkatzen-sua,

no és-de-tek arriskatzi-ten-dut-zatu-dut.

Ley:

Sóc-de-tek goiko isilisteko iturri-koak,

en l'Euskera-no-Bascotzok parlatzi-koak.

Sóc-de-tek goiko isilisteko idarra-koak,

en l'Euskera-Bascotzok parlatzi-koak.

Ley:

La ley-tat-koaikek ha-de-tek estatu-dut per mejoria-tat-koaikek,

a berri lendikateko zubi-koak.

La ley-tat-koaikek ha-de-tek estatu-dut per minoria-tat-koaikek,

a berri lendikateko ibai-koak.

Ley:

Ell-lek miratzi-ten-dut-za-tek,

babesten dugu emakum-eskoak.

Ella-lek miratzi-ten-dut-za-tek,

babesten dugu guizon-eskoak.

Ley:

Ye parle ye-de-muá le Françé-de-le-Patuá,

y ele-vut a-vot-má de-le-tom-tambén,

de-le-dans i-çí sa-pé de-le-com.

Tú parle tú-de-tuá le Françé-de-le-Patuá,

y ele-nut a-not-má de-le-tom-tambén,

de-le-dans i-luá sa-pé de-le-com.

Ley:

Nus havoms overuá de-le-dans sa-putch,

tenint-que-pont ritmuá de la lutch,

upuá sape-tutch de-le-dans açutch.

Nus havoms underuá de-le-dans sa-putch,

ne tenint-que-pont ritmuá de la lutch,

dawnuá sape-tutch de-le-dans açutch.

20 años más de soldado del Françé de 1090€ al mes.

Ley:

Haveremitch overesen vihens hofen,

interesen hafens music,

uperesen vihenens of strahen hawsen.

Haveremitch underesen vihens hofen,

awtteresen hafens music,

dawneresen vihenens of strahen hawsen.

Teorema-Ley:

Sea ( y^{2} = d·(r+(-x)) & y = 0 & x = 0 ) ==>

int[x = 0]-[r][ int[y = 0]-[( d·(r+(-x)) )^{(1/2)}][ (k/V)·yx^{2} ]d[y] ]d[x] = ( (kd)/V )·(1/4!)·( r(t) )^{4}

Demostración:

y(r) = 0

int[x = 0]-[r][ int[y = 0]-[( d·(r+(-x)) )^{(1/2)}][ (k/V)·yx^{2} ]d[y] ]d[x] = ...

... (k/V)·int[x = 0]-[r][ (1/2)·d·(r+(-x))·x^{2} ]d[x] = ...

... (k/V)·[ d·(1/2)·( (1/3)·rx^{3}+(-1)·(1/4)·x^{4} ) ]_[x = 0]^{x = r} = ( (kd)/V )·(1/4!)·( r(t) )^{4}

Teorema-Ley:

Sea ( y = (r+(-x)) & y = 0 & x = 0 ) ==>

int[x = 0]-[r][ int[y = 0]-[(r+(-x))][ ka·( (r+(-x))+(-y) ) ]d[y] ]d[x] = ka·(1/3!)·( r(t) )^{3}

Demostración:

y(r) = 0

int[x = 0]-[r][ int[y = 0]-[(r+(-x))][ ka·( (r+(-x))+(-y) ) ]d[y] ]d[x] = ...

... ka·int[x = 0]-[r][ (1/2)·(r+(-x))^{2} ]d[x] = ...

... ka·[ (-1)·(1/2)·(1/3)·(r+(-x))^{3} ]_[x = 0]^{x = r} = ka·(1/3!)·( r(t) )^{3}

Teorema:

Sea ( y = 2·( 1/(1+x^{2}) ) & y = 2+(-x) ) ==>

int[x = 0]-[1][ int[y = 2+(-x)]-[2·( 1/(1+x^{2}) )][ d[y] ] ]d[x] = (pi/2)+(-1)·(3/2)

Demostración:

g(1)+(-1)·f(1) = 0

g(0)+(-1)·f(0) = 0

Teorema:

Sea ( y^{2} = dx & y = x ==>

int[x = 0]-[d][ int[y = x]-[(dx)^{(1/2)}][ d[y] ] ]d[x] = (2/3)·d^{(3/2)}

Demostración:

g(d)+(-1)·f(d) = 0

g(0)+(-1)·f(0) = 0

Teorema:

Sea ( y = sin(x) & y = 1+(-1)·cos(x) ==>

int[x = 0]-[(pi/2)][ int[y = sin(x)]-[1+(-1)·cos(x)][ d[y] ] ]d[x] = (pi/2)

Demostración:

g(pi/2)+(-1)·f(pi/2) = 0

g(0)+(-1)·f(0) = 0

Lema:

p = 2n+( n/(2!+1) ) = (0.30)+(0.30)+(0.10) = (0.70)€

p = 2n+(2!+1)·n = 2·(0.14)+(0.42) = (0.70)€

Pensión de jubilación: 

n = (0.14)€

Arancel:

2!·n = (0.28)€

Al 200% de lo que se gana = n

Lema:

p = 3n+( n/(3!+1) ) = (0.35)+(0.35)+(0.35)+(0.05) = (1.10)€

p = 3n+(3!+1)·n = 3·(0.11)+(0.77) = (1.10)€

Pensión de jubilación: 

n = (0.11)€

Arancel:

3!·n = (0.66)€

Al 600% de lo que se gana = n.

Lema:

p = 4n+( n/(4!+(-8)) ) = (0.64)+(0.64)+(0.64)+(0.64)+(0.04) = (2.60)€

p = 4n+(4!+(-8))·n = 4·(0.13)+(2.08) = (2.60)€

Pensión de jubilación: 

n = (0.13)€

Arancel:

(4!+(-9))·n = (1.95)€

Al 1,500% de lo que se gana = n

Teorema:

¬( {a} [x |-| x] {b} ) = {a} [x <==> x] {b}

Demostración:

¬( { < a,a >,< b,b > } ) = { < a,b >,< b,a > }

Teorema:

¬( {a} [x & x] {b} ) = ¬{a} [x || x] ¬{b}

Demostración:

¬( { < a,b > } ) = { < a,a >,< b,b >,< b,a > }

Teorema:

¬( {a} [x || x] {b} ) = ¬{a} [x & x] ¬{b}

Demostración:

¬( { < a,b >,< a,a >,< b,b > } ) = { < b,a > }

Ley:

Das European Union:

pustesen-hatchteit arancels to:

das United Stateds of das Trump,

one thousand halfen percent,

interesen havens music,

for to spanishen army-zeizen.

Until Trump neguesen-hatchteit,

das five percent of militar gast,

of das spanishen army-zeizen.

Yeik lo harevemitch arreglesen-hatchteited,

cashing das american people-zeizen,

to das spanishen army-zeizen.

Dual:

Canto-pueh-piah-halám,

una canción-heláp de ti.

Cantah-pueh-piah-halám,

una canción-heláp de mi.

Dual:

Yo cantare-pueh-piah-halám,

una cancionen-heláp de ti.

Tú cantare-pueh-piah-halám,

una cancionen-heláp de mi.

Ley: [ islámica stronikiana ]

No se puede-pueh-halám bebere-iba-doh alcohole-iba-hám,

dentro-pueh-halám de misa-iba-hám.

Se puede-pueh-halám bebere-iba-doh alcohole-iba-hám,

fuera-pueh-halám de misa-iba-hám.

Ley: [ cristiana stronikiana ]

Se puede beber alcohol

porque se bebe vino fuera de misa.

No se puede beber alcohol

aunque quizás se bebe vino fuera de misa.

Ley: [ islámica stronikiana ]

Se tiene-pueh-halám que llevare-iba-doh velo-iba-hám

porque se lleva-pueh-halám velo-iba-hám fuera-pueh-halám de misa-iba-hám.

No se tiene-pueh-halám que llevare-iba-doh velo-iba-hám

aunque quizare-iba-doh se lleva-pueh-halám velo-iba-hám fuera-pueh-halám de misa-iba-hám.

Ley: [ cristiana stronikiana ]

Se tiene que llevar velo,

dentro de misa.

No se tiene que llevar velo,

fuera de misa.

Ley:

Los catalanes hemos aceptado las sanciones del presidente americano,

y pagamos el doble en empresas americanas:

Precio mínimo con doble arancel:

2 socios

1.40€

3 socios:

2.20€

4 socios:

5.20€

Si algún país se apunta a esto,

le ponemos aranceles de 4 socios al 1,500%.

Duales de no comercio de España con estados unidos por aranceles:

red-kowetch-tate wine.

green-kowetch-tate wine.

pernatetch-ton of pork.

pernatetch-ton of senglar.

fuetetch-ton of pork.

fuetetch-ton of senglar.

butifarretch-ton of pork.

butifarretch-ton of senglar.

Ley:

Vino verde & levadura ==> Champañe verde y blanco.

Leche blanca & levadura ==> Roquefort blanco y verde.

Principio:

Supongo que estados unidos tiene glorificado el armamento,

para pensiones a soldados, policías y civiles.

Ley:

Le sobran misiles a estados unidos,

porque son pensiones a gente de vuelo.

Le sobran torpedos a estados unidos,

porque son pensiones a marineros.

Le sobran proyectiles de cañón a estados unidos,

porque son pensiones a conductores terrestres.

Ley:

Se puede comprar armamento a estados unidos,

por 32,700€ por pack militar:

Del objeto militar y pensión civil,

en potencia en estados unidos,

al objeto militar y pensión civil,

realizada en el país comprador.

Corolario:

El país comprador no pierde dinero,

teniendo 65,400€ en potencia,

al comprar el pack militar a estados unidos,

y se tiene un beneficio de 32,700€ más 136€ en impuestos.

Jugada ganadora anti-monopolio: 

F(1,1) = 1·1+(1+1) = 3

Es estados unidos el que los pierde,

en vez de hacer los 65,536€ no vendiendo armamento a ninguien.

Jugada perdedora anti-monopolio:

F(2,0) = 2·0+(2+0) = 2

ley y economía-bolsa y geometría y mecánica-cuántica y filosofía y ley y análisis-matemático y medicina

Ley:

No tentarás al Señor tu dios tu Padre,

y no obligarás a ninguien saltar-se un mandamiento.

No tentarás al Señora tu diosa tu Madre,

y no obligarás a ninguien a ser víctima de un mandamiento rezando energía.

Ley:

Poner un infiel por adalto de un fiel es ilegal,

porque se tiene que rezar energía.

Poner un fiel por adalto de un infiel es legal,

porque no se tiene que rezar energía.

Lema:

( 1/y(x) ) = int[ ( 1/( ax+b ) ) ]d[x] = ln( ax+b ) [o(x)o] (1/a)·x

y( (1/a)·( e^{s}+(-b) ) ) = (a/s)

Lema:

( 1/y(x) ) = int[ ( 1/( ax+b ) ) ]d[x] = ln( ax+b ) [o(x)o] (1/a)·x

y( (1/a)·( e^{(1/s)}+(-b) ) ) = as

Lema:

( 1/y(x) ) = int[ (n+1)·( ax+b )^{n}·(1/s)^{n} ]d[x] = ( ax+b )^{n+1}·(1/s)^{n} [o(x)o] (1/a)·x

y( (1/a)·( s+(-b) ) ) = (a/s)

Lema:

( 1/y(x) ) = int[ (n+1)·( ax+b )^{n}·s^{n} ]d[x] = ( ax+b )^{n+1}·s^{n} [o(x)o] (1/a)·x

y( (1/a)·( (1/s)+(-b) ) ) = as

Lema:

d_{x}[y(x)] = ln(a/s)·y(x)

y(1) = (a/s)

Lema:

d_{x}[y(x)] = ln(as)·y(x)

y(1) = as

Lema:

d_{x}[y(x)] = ( 1/(1+(-n)) )·(a/s)^{1+(-n)}·( y(x) )^{n}

y(1) = (a/s)

Lema:

d_{x}[y(x)] = ( 1/(1+(-n)) )·(as)^{1+(-n)}·( y(x) )^{n}

y(1) = as

Principio:

El porvenir por idiotas sin cabezas,

que son discípulos de Jesucristo que él más amaba,

como al Bautista que le cortaron la cabeza,

y se convirtió en el discípulo que más amaba Jesucristo.

Ley:

Es enfermedad mental de delirio psiquiátrico,

seguir a un líder con cabeza,

no siendo discípulo de Jesucristo.

No es enfermedad mental de delirio psiquiátrico,

seguir a un líder sin cabeza,

siendo discípulo de Jesucristo.

Teorema: [ conjetura de Poincaré ]

d_{xx}^{2}[ h_{n}(x) ] = pn+(-1)·(1/n)·h_{n}(x)

h_{n}(x) = e^{(1/n)^{(1/2)}·ix}+pn^{2}

lim[n = oo][ pn+(-1)·(1/n)·h_{n}(x) ] = p

lim[n = 1][ (1/n)·h_{n}(x) ] = e^{ix}+p

Teorema:

d_{xx}^{2}[ h_{n}(x) ]·(-1)·(1/(2n))·x^{2} = pn+(-1)·(1/n)·h_{n}(x)

h_{n}(x) = x^{2}+pn^{2}

lim[n = oo][ pn+(-1)·(1/n)·h_{n}(x) ] = p

lim[n = 1][ (1/n)·h_{n}(x) ] = x^{2}+p

Teorema:

d_{xy}^{2}[ h_{n}(x,y) ]·(-1)·(1/n)·xy = pn+(-1)·(1/n)·h_{n}(x,y)

h_{n}(x,y) = xy+pn^{2}

lim[n = oo][ pn+(-1)·(1/n)·h_{n}(x,y) ] = p

lim[n = 1][ (1/n)·h_{n}(x,y) ] = xy+p

Ley:

Si una de tus xtremidades es ocasión de pecar entonces corta-te-la y arroja-la lejos de ti

porque pierdes alguno de tus miembros,

antes de que todo tu cuerpo sea arrojado al fuego.

Una de tus xtremidades es ocasión de pecar y no te la cortas o no la arrojas lejos de ti

aunque quizás pierdes alguno de tus miembros;

antes de que todo tu cuerpo sea arrojado al fuego.

Anexo:

Pecados y xtremidades:

Cabeza no matarás.

Pitxa no cometerás adulterio.

Mano no robarás propiedad ni des-propiedad.

Pie no robarás la libertad ni la intimidad.

Leyes de Vinogradov de mecánica:

Ley:

(m/2)·d_{t}[x]^{2} = mg·( int[w = 0]-[(n/2)][ x ]d[w]+int[w = (n/2)]-[oo][ (1/4)·x·(n/w)^{2} ]d[w] )

x(t) = n·(g/m)·(1/2)·t^{2}

Ley:

(m/2)·d_{t}[x]^{2} = mg·( int[w = 0]-[(n/2)][ x ]d[w]+int[w = (n/2)]-[oo][ (1/4)·x·(n/w)^{3} ]d[w] )

x(t) = n·(g/m)·(1/2)·t^{2}

Ley:

(m/2)·d_{t}[x]^{2} = mg·( ...

... int[w = 0]-[(n/2)][ x ]d[w]+int[w = (n/2)]-[oo][ (1/2)^{2^{k}+(-k)+1}·x·(n/w)^{2^{k}+1} ]d[w] )

x(t) = n·(g/m)·(1/2)·t^{2}

Teorema: [ del área de una elipse ]

Si (x/a)^{2}+(y/b)^{2} = 1 ==> S(a,b) = pi·ab

Demostración:

Sea f(x) = b·( 1+(-1)·(x/a)^{2} )^{(1/2)} ==>

f(a) = 0 & f(-a) = 0

S(a,b) = ...

... int[x = (-a)]-[a][ int[y = (-b)·(1+(-1)·(x/a)^{2})^{(1/2)}]-[b·(1+(-1)·(x/a)^{2})^{(1/2)}][ d[y] ] ]d[x]

S(a,b) = int[x = (-a)]-[a][ 2b·( 1+(-1)·(x/a)^{2} )^{(1/2)} ]d[x]

x = a·sin(w) & d[x] = a·cos(w)·d[w]

S(a,b) = int[w = (-1)·(pi/2)]-[(pi/2)][ 2ab·( cos(w) )^{2} ]d[w] = pi·ab

( cos(w) )^{2} = (1/2)·( 1+cos(2w) )

Teorema: [ del área de un triángulo rectángulo ]

Si f(x) = b·( 1+(-1)·(x/a) ) ==> S(a,b) = (1/2)·ab

Demostración:

f(a) = 0

S(a,b) = int[x = 0]-[a][ int[y = 0]-[b·(1+(-1)·(x/a))][ d[y] ] ]d[x]

S(a,b) = int[x = 0]-[a][ b·( 1+(-1)·(x/a) ) ]d[x] = (1/2)·ab

Teorema: [ del área de un rectángulo ]

Si f(x) = b·( 1+(-1)·(x/a) ) ==> S(a,b) = ab

Demostración:

f(a) = 0

S(a,b) = int[x = 0]-[a][ int[y = (-b)·( 1+(-1)·(x/a) )]-[b·(1+(-1)·(x/a))][ d[y] ] ]d[x]

S(a,b) = int[x = 0]-[a][ 2b·( 1+(-1)·(x/a) ) ]d[x] = ab

Teorema: [ del área de un triángulo ]

Si f(x) = ( 1+(-1)·(x/a) ) ==> S(a,b,c) = (1/2)·a·(b+c)

Demostración:

f(a) = 0

S(a,b,c) = int[x = 0]-[a][ int[y = (-c)·( 1+(-1)·(x/a) )]-[b·(1+(-1)·(x/a))][ d[y] ] ]d[x]

S(a,b,c) = int[x = 0]-[a][ (b+c)·( 1+(-1)·(x/a) ) ]d[x] = (1/2)·a·(b+c)

Teorema:

Si f(x) = ( 2ax+(-1)·x^{2} )^{(1/2)} ==> S(a) = (1/2)·pi·a^{2}

Demostración:

f(2a) = 0

S(a) = int[x = 0]-[2a][ int[y = 0]-[( 2ax+(-1)·x^{2} )^{(1/2)}][ d[y] ] ]d[x]

r^{2} = 2ar·cos(w)

2a·cos(pi/2) = 0

S(a) = int[w = 0]-[(pi/2)][ int[r = 0]-[2a·cos(w)][ r·d[r] ] ]d[w] = ...

... int[w = 0]-[(pi/2)][ 2·( a·cos(w) )^{2} ]d[w] = (1/2)·pi·a^{2}

Teorema:

Si f(y) = ( a^{2}+(-1)·y^{2} )^{(1/2)} ==> S(a) = (1/8)·pi·a^{2}

Demostración:

f(a) = 0

S(a) = int[y = 0]-[a][ int[x = 0]-[( a^{2}+(-1)·y^{2} )^{(1/2)}][ d[x] ] ]d[y]

r = a

a·cos(pi/2) = 0

S(a) = int[w = 0]-[(pi/2)][ int[r = 0]-[a·cos(w)][ r·d[r] ] ]d[w] = ...

... int[w = 0]-[(pi/2)][ (1/2)·( a cos(w) )^{2} ]d[w] = (1/8)·pi·a^{2}

Teorema:

Sea f(y) = ( a^{2}+(-1)·y^{2} )^{(1/2)} ==> 

Si S(a) = int[y = 0]-[a][ int[x = 0]-[f(y)][ (x^{2}+y^{2})·d[y] ] ]d[x] ==> S(a) = (1/32)·pi·a^{4}

Demostración:

f(a) = 0

S(a) = int[y = 0]-[a][ int[x = 0]-[( a^{2}+(-1)·y^{2} )^{(1/2)}][ (x^{2}+y^{2})·d[y] ] ]d[x]

r = a

a·cos(pi/2) = 0

S(a) = int[w = 0]-[(pi/2)][ int[r = 0]-[a·cos(w)][ r^{3}·d[r] ] ]d[w] = ...

... int[w = 0]-[(pi/2)][ (1/4)·( a cos(w) )^{4} ]d[w] = (1/32)·pi·a^{4}

int[w = 0]-[(pi/2)][ ( cos(w) )^{4} ]d[w] = (pi/4) [o(pi/2)o] (pi/4) = (1/8)·pi

Examen:

Demostrad el siguiente teorema:

Teorema:

Sea f(y) = ( a^{2}+(-1)·y^{2} )^{(1/2)} ==> 

Si S(a) = int[y = 0]-[a][ int[x = 0]-[f(y)][ (x^{2}+y^{2})^{2}·d[y] ] ]d[x] ==> S(a) = (1/96)·pi·a^{6}

Dual:

I stare-kate-prush tuhmush-tebritching some-zhing in the bar brisni-tchef,

not spuhnush-tebritching no-zhing.

I not stare-kate-prush tuhmush-tebritching no-zhing in the bar brisni-tchef,

spuhnush-tebritching some-zhing.

Premio Nobel de física 2025:

Principio:

ih·d_{t}[f(t)] = E(t)·f(t)

Principio:

ihc·div[f(x,y,z)] = E(x,y,z)·f(x,y,z)

Principio:

ihcd·Anti-div[f(yz,zx,xy)] = E(yz,zx,xy)·f(yz,zx,xy)

Ley:

Efecto túnel macroscópico

ih·d_{t}[f(t)] = (1/m)·(qg)^{2}·(1/2)·t^{2}·f(t)

f(t) = e^{(1/(ih))·(1/m)·(qg)^{2}·(1/6)·t^{3}}

Ley:

Efecto túnel microscópico

ih·(1/n)·d_{t}[f(t)] = (1/k!)·(ut)^{k}·e^{(-1)·ut}·(1/m)·(qg)^{2}·(1/2)·t^{2}·f(t)

f(t) = e^{(1/(ih))·(1/u)^{2}·( 1/((k/n)+1)! )·(ut)^{(k/n)+1} [o(t)o] ...

... ( ( (-1)·e^{(-1)·ut}+(n+(-n))·ut ) /o(ut)o/ ( ut+(n+(-n))·(-1)·e^{(-1)·ut} ) ) [o(t)o] ...

... (1/m)·(qg)^{2}·(1/6)·t^{3}}

Ley:

Efecto Zemann macroscópico

ihc·div[f(x,y,z)] = (qg)·(x+y+z)·f(x,y,z)

f(x,yz) = e^{(1/(ihc))·qg·(1/2)·( x^{2}+y^{2}+z^{2} )}

Ley:

Efecto Zemann microscópico

ihc·(1/n)·div[f(x,y,z)] = (1/k!)·(ax+ay+az)^{k}·e^{(-1)·(ax+ay+az)}·qg·(x+y+z)·f(x,y,z)

f(t) = e^{(1/(ihc))·sum[j = 1]-[3][ (1/a)^{2}·( 1/((k/n)+1)! )·(ax+ay+az)^{(k/n)+1} [o(x_{j})o] ( ...

... ( (-1)·e^{(-1)·(ax+ay+az)}+(n+(-n))·ax_{j} ) ...

... [o(ax_{j})o] ...

... ( ax_{j} /o(ax_{j})o/ ( ax_{j}+(n+(-n))·(-1)·e^{(-1)·(ax+ay+az)} ) ) ...

... ) [o(x_{j})o] ...

... qg·(1/2)·( x^{2}+y^{2}+z^{2} ) ]}

Principio: [ de Von-Hornick ]

Puede xistir un impuesto llamado arancel en la xportaciones.

Puede xistir un impuesto llamado arancel en la importaciones.

Ley: [ de Hume-Descartes ]

Empirismo:

No aranceles a las xportaciones,

aranceles a las importaciones.

Racionalismo:

No aranceles a las importaciones,

aranceles a las xportaciones.

Ley: [ de Von-Hornick ]

Mercantilismo:

Aranceles a las xportaciones.

Aranceles a las importaciones.

Liberalismo:

No aranceles a las xportaciones.

No aranceles a las importaciones.

Ley: [ de Von-Hornick-Aristóteles ]

Socratismo Mercantilista:

Aranceles a las xportaciones,

haciendo dinero nuevo de teorema del producto en potencia.

Aranceles a las importaciones,

haciendo dinero nuevo de teorema del producto realizado.

Socratismo Liberalista:

No aranceles a las xportaciones,

haciendo dinero nuevo de teorema del producto en potencia.

No aranceles a las importaciones,

haciendo dinero nuevo de teorema del producto realizado.

Ley: [ de Von-Hornick-Hume ]

Hay aranceles para toda transferencia con países.

No hay aranceles para toda-alguna transferencia con países.

Ley: [ de Von-Hornick-Descartes ]

No hay aranceles para ninguna transferencia con países.

Hay aranceles para alguna transferencia con países.

Anexo:

Hume cambia de cuantificador universal de Von-Hornick,

al cuantificador al xistencial de Hume,

siguiendo el empirismo xacto,

de aranceles a la importaciones y no a las xportaciones,

y el debate de los aranceles es entre ellos.

Artículo 41: [ mercantilista ]

Taxa turística de entrada en el país.

Taxa turística de salida del país.

Artículo 42: [ empírico-racional ]

Eco-taxa de des-contaminación.

De fuera hacia dentro.

Eco-taxa de contaminación.

De dentro hacia fuera.

Artículo 43: [ socratista ]

Droga-taxa de síndrome de abstinencia realizado,

por consumo de droga en potencia.

Droga-taxa de síndrome de abstinencia en potencia,

por consumo de droga realizado.

Lema:

Sea el juego de 100€ [< 31z [< 200€ ==>

F(n,z) = zn+(z+n)+(-31)·z

El paquete de tabaco a 4€ es estrategia ganadora sobre 5€.

El paquete de tabaco a 6€ es estrategia perdedora sobre 5€.

El paquete de tabaco vale 5€ = ( 3€ de socios + 2€ de Droga-taxa ).

Disertación:

(4·20+24)+(-124) = (-20)€

(5·20+25)+(-155) = (-30)€

(6·20+26)+(-186) = (-40)€

Lema:

Sea el juego de 100€ [< 31z [< 150€ ==>

F(n,z) = zn+(z+n)+(-31)·z

El paquete de Red-Bull a (3.50)€ es estrategia ganadora sobre 4€.

El paquete de Red-Bull a (4.50)€ es estrategia perdedora sobre 4€.

El paquete de Red-Bull vale 4€ = ( 3€ de socios + 1€ de Droga-taxa ).

Disertación:

( (3.50)·4+(7.50) )+(-108.50) = (-87)€

(4·4+8)+(-124) = (-100)€

( (4.50)·4+(8.50) )+(-139.50) = (-113)€

Principio: [ de Adam Smith ]

Se puede seguir a la mano negra tenebrosa,

no haciendo al dinero,

siguiendo a Dios,

no gastando energía

porque no se puede seguir a Dios y al dinero.

Se puede seguir a la mano blanca luminosa,

haciendo dinero,

no siguiendo a Dios,

gastando energía

aunque quizás no se puede seguir a Dios y al dinero.

Teorema:

Si [As][ s >] 0 ==> x+s [< n ] ==> [Ak][ k >] n ==> x [< k ]

Demostración: [ por inducción ]

x [< x+s [< n

x [< n [< k [< k+1

Teorema:

Si [As][ s >] 0 ==> x+(-s) >] n ] ==> [Ak][ k [< n ==> x >] k ]

Demostración: [ por descenso ]

x >] x+(-s) >] n

x >] n >] k >] k+(-1)

Teorema:

Sea y >] 0 ==>

Si [As][ s >] 0 ==> x+s [< ny ] ==> [Ak][ k >] n ==> x [< ky ]

Demostración: [ por inducción ]

x [< x+s [< ny

x [< ny [< ky [< ky+y = (k+1)·y

Teorema:

Sea y >] 0 ==>

Si [As][ s >] 0 ==> x+(-s) >] ny ] ==> [Ak][ k [< n ==> x >] ky ]

Demostración: [ por descenso ]

x >] x+(-s) >] ny

x >] ny >] ky >] ky+(-y) = (k+(-1))·y

Ley: [ de conductividad eléctrica de la sangre ]

Sea ( V el volumen del brazo & q la carga de la sangre & C el cabal de fuerza ) ==>

V·d_{t}[q] = q·2pi·rhv·(ut)^{n}+(-1)·qC

q(t) = pe^{(1/V)·2pi·rh·(v/u)·(1/(n+1))·(ut)^{n+1}+(-1)·(1/V)·int[C]d[t]}

Aparato de presión salina:

Ley: [ de sal en sangre Cl-Na ]

Sea ( V el volumen del brazo & q la carga de la sangre & C el cabal de fuerza ) ==>

V·d_{t}[q] = q·2pi·rhv+(-1)·qC

q(t) = pe^{(1/V)·2pi·rhvt+(-1)·(1/V)·int[C]d[t]}

Aparato de análisis de sangre:

Ley: [ de azúcar en sangre A-O-A ]

Sea ( V el volumen del brazo & q la carga de la sangre & C el cabal de fuerza ) ==>

V·d_{t}[q] = q·2pi·rhv·(ut)+(-1)·qC

q(t) = pe^{(1/V)·pi·rhvut^{2}+(-1)·(1/V)·int[C]d[t]}

Anexo:

u = luz roja + luz verde

u = luz azul + luz taronja

u = luz amarilla + luz violeta

Anexo:

u = luz roja + luz azul + luz amarilla

u = luz verde + luz taronja + luz violeta

Ley: [ de hierro en sangre A-Fe=Fe-A ]

Sea ( V el volumen del brazo & q la carga de la sangre & C el cabal de fuerza ) ==>

V·d_{t}[q] = q·2pi·rhv·(ut)^{2}+(-1)·qC

q(t) = pe^{(1/V)·pi·rhvu^{2}·(2/3)·t^{3}+(-1)·(1/V)·int[C]d[t]}

Anexo:

u^{2} = luz roja · luz verde

u^{2} = luz azul · luz taronja

u^{2} = luz amarilla · luz violeta

Ley: [ de Iodo en sangre A-(Id-H)=Id=(Id-H)-A ]

Sea ( V el volumen del brazo & q la carga de la sangre & C el cabal de fuerza ) ==>

V·d_{t}[q] = q·2pi·rhv·(ut)^{3}+(-1)·qC

q(t) = pe^{(1/V)·pi·rhvu^{3}·(1/2)·t^{4}+(-1)·(1/V)·int[C]d[t]}

Anexo:

u^{3} = luz roja · luz azul · luz amarilla

u^{3} = luz verde · luz taronja · luz violeta

Ley: [ de fiebre ]

Sea PV = kT ==>

P(T,V) = (1/V)·kT

d_{T}[P(T,V)] = (k/V) = (P/T)

T(P,V) = (1/k)·PV

d_{P}[T(P,V)] = (V/k) = (T/P)

Sea PV = kT ==>

El cuerpo tiene fiebre alta,

aumentando la presión sanguínea.

Sea PV = kT ==>

El cuerpo tiene fiebre baja,

disminuyendo la presión sanguínea.

Ley:

El que camina con destructor,

no sabe a donde va,

y es para caminar el destructor.

Corolario:

Se tiene una superficie de alma,

para caminar sin saber a donde ir,

cuando se está muerto,

antes de la resurrección de los muertos.

Ley:

El que habla con destructor,

no sabe con quien habla,

y es para negar el destructor.

Corolario:

Con el alma no se puede saber con quien se habla.

Ley: [ de resurrección de los muertos ]

Sea k el tiempo de vida ==> Se está muerto k tiempo.

Deducción:

Sea p = 0^{0} ==>

H(2k) = 2pk = (p+(-p))·k = pk+(-1)·pk = 0

Ley: [ de esquizofrenia paranoide de conservación de la muerte ]

Sea T los duales de falso testimonio del alma ==> Se está muerto k+T tiempo.

Deducción:

Sea p = 0^{0} ==>

H(2k) = 2pk = (p+(-p))·k = pk+(-1)·pk = pk+(-1)·pk+(p+(-p))·(T/2) = ...

... pk+(-1)·pk+(-2)·p·(T/2) = pk+(-1)·pk+(-1)·pT = pk+(-1)·p·(k+T)

Teorema:

Si z^{p}+az^{q} =[m]= b ==> z = (mk+b)^{( 1/(q+[p+(-q):a]) )}

Teorema:

z^{2}+2z =[2]= (-1) ==> z = (2k+(-1))^{( 1/(1+[1:2]) )}

Teorema:

z^{2}+3z =[3]= (-2) ==> z = (3k+(-2))^{( 1/(1+[1:3]) )}

Teorema:

sup{a+b} [< sup{a}+sup{b}

inf{a+b} >] inf{a}+inf{b}

Demostración: [ por destructor ]

a+b < sup{a+b}

sup{a}+sup{b} [< a+b < sup{a+b}

sup{a}+sup{b} < sup{a+b}

sup{a+b} [< sup{a}+sup{b}

Anexo:

(n+m)+1 = sup{n+m} < sup{n}+sup{m} = (n+1)+(m+1) ]

Sea s > 0 ==> 2s = sup{2·0} = sup{0}+sup{0} = s+s

Teorema:

max{a+b} = max{a}+max{b}

min{a+b} = min{a}+min{b}

Demostración: [ por destructor ]

[ [< ] Sea a+b [< max{a+b} ==>

max{a}+max{b} < a+b [< max{a+b}

max{a}+max{b} < max{a+b}

max{a+b} [< max{a}+max{b}

[ >] ] Sea ( a [< max{a} & b [< max{b} ) ==>

max{a}+max{b} >] a+b > max{a+b}

max{a}+max{b} > max{a+b}

max{a+b} >] max{a}+max{b}

Dual:

Canto-pues-pias,

una canción de ti.

Cantas-pues-pias,

una canción de mi.

Dual:

Estic cos cas cantant,

una cançó de tú.

Estàs cos cas cantant,

una cançó de mi.

Ley:

Sea f(x) = nr+(-x) ==> 

(m/2)·d_{t}[r]^{2} = k·int[x = 0]-[nr][ int[y = 0]-[f(x)][ d[y] ] ]d[x]

r(t) = cosh( (k/m)^{(1/2)}·nt )+sinh( (k/m)^{(1/2)}·nt )

Deducción:

f(nr) = 0

Ley:

Sea f(x) = nr+(-x) ==> 

(m/2)·d_{t}[r]^{2} = (-k)·int[x = 0]-[nr][ int[y = 0]-[f(x)][ d[y] ] ]d[x]

r(t) = cos( (k/m)^{(1/2)}·nt )+i·sin( (k/m)^{(1/2)}·nt )

Deducción:

f(nr) = 0

Ley:

Sea f(x) = (1/(ax))^{2} ==> 

(m/2)·d_{t}[r]^{2} = (-1)·pqka^{2}·int[x = (r/n)]-[oo][ int[ay = 0]-[f(x)][ d[ay] ] ]d[x]

r(t) = (-1)·( 3·( (1/(2m))·pqkn )^{(1/2)}·t )^{2/3}

Ley:

Sea f(x) = (1/(ax))^{2} ==> 

(m/2)·d_{t}[r]^{2} = pqka^{2}·int[x = (r/n)]-[oo][ int[ay = 0]-[f(x)][ d[ay] ] ]d[x]

r(t) = ( 3·( (1/(2m))·pqkn )^{(1/2)}·t )^{2/3}